There are old house lovers and there are new construction lovers. Often members of each group think the others are nuts and just don't understand why anyone would want that junk.  Your coworker is a new construction person and their approach is remove and replace everything. If you find an old house lover to go through with you then you will get a different view of what must be replaced. 
Knob and tube wiring does not need to be actually removed.  Once it is disconnected, it can be left where it isn't easily accessible to remove. A good old house electrician will have some good ideas about where to run new wire and how to get wires into the appropriate places with the minimum amount of damage. Just be sure the workers don't do anything like cut baseboard or crown. Instead if they need access behind the trim, ask them to let you know and you can carefully remove it for reinstalling later.  If you have thick baseboard, they may be able remove it and cut a slot of sufficient size to cover Romex along the wall. If you don't like the proposed solution then ask to discuss alternatives

The first priority is to disconnect the knob and tube wiring. Hopefully the electrician is able to run new wiring without too much damage to the walls. Mini splits are a good solution to provide cooling to a 110 year old house. Are you getting a heat pump which can also be used for heating? It may cost less to heat the house with the mini splits instead of your current heating system. The current system could be backup heating for very cold days.

The guy you spoke to probably has never mixed a batch of plaster and does not know how to fix plaster walls. It is probably best to wait until all the wall penetrations have been done before getting quotes for repairs.

In the mean time here is video showing how a plaster wall can be repaired at a low cost:

How to Repair Plaster Walls | This Old House

Thank you very much for your responses. I did know that they don't have to actually remove the knob and tube, just disconnect it and install new wiring. This is what the electrician I haven't actually hired yet is planning on doing. I was hoping this guy was willing to do more patch work, but obviously I was wrong. I'm looking for someone that is good at old house stuff, but not having much luck. If someone has a recommendation in Massachusetts, please feel free to share contact info. And I'm definitely willing to do some of the work myself, as well. I am not a stranger to plaster, paint or wall paper, but my carpentry and construction skills are more in line with "it's just a barn" not "it's in the dining room."

We are getting the minisplits that also have a heat pump. So we will be able to use them for heating, but as the HVAC guy said, you would want to maintain the current system (city gas with forced hot water) because the heat pump won't keep up with temps in the single digits.

We are also in MA and had the mini splits installed first week of Jan. Had our gas steam boiler removed last week. The mini splits absolutely keep the house WARM. Like 72 degrees warm when it was below zero with the wind chill. We had 2 condensers installed and 6 splits (1 in basement, 2 on main floor, 3 upstairs in the bedrooms). We mostly keep the bedroom units off bc it gets too hot up there. We have plenty of insulation in the attic and walls.

Keep looking for contractors that handle plaster. You can use blue board with skim coat of plaster. Everyone we have used over the last 15 years has been fine with plaster repair.

In MA you can also get a Heat Loan for zero interest up to a certain amount to put in the mini splits. To do the heat and remove your boiler you’ll need a bigger more expensive condenser unit. Try another quote from a different mini split person.

We have 1930s plaster and have had plenty of holes made and repaired in the 35 years we have lived here. I have found that workers used to older homes and cutting into plaster are careful about how they cut, avoiding too much vibration. One cut the entire hole for a wall furnace by hand!

I can do small repairs. When we had major cracks following foudation replacement I hired a plaster specialist who matched the finish perfectly.

We now have mini splits instead of the wall furnace. Wall furnace hole was patched. No plaster repair was needed after mini split installation.

I live in Mass and have seen great plaster repairs done by painting contractors. If you want museum quality work you will pay through the nose but if you want a finished job that will look fine when carpet and upholstery and wall hangings and mini splits are added, you probably will be happy with the repair work done by almost painter who has worked in old houses around here. Get the electrician to tell you where and what size the holes will be and then get an estimate from the painting contractor. I'm an old house lover rather than a new construction lover but beware that if you do the stairwell as a complete gut job there may be lead paint issues with the process.

Agree that the trick with old homes is to always try to work with crafts people who specialize in older homes. I just finished restoring plaster ceilings, repairing some walls, and interior painting in my 1928 home. I used a painting contractor who specializes in old homes. The work was labor intensive and expensive but turned out beautifully. When remodeling the kitchen and bathroom my GC had subs who know how to make old homes sing. Finding the right contractors is key. Good luck with your project.

I live in the Boston burbs and actually find it easier to find a plasterer than someone who will do residential drywall-- not that I would want that! Plaster is relatively easy and forgiving to repair. Easier than getting an invisible repair in drywall in my experience. Pass on anyone who tells you it's hard or impossible, a sure giveaway that they don't know what they are talking about. Around here I have not found it to be more expensive-- the guys who do it like the once and done work, and really hate the "come back and sand" multiple time routine.

This is great to hear. We are getting a HEAT loan to do the minisplits and replace the wiring. I’ve had 2 HVAC guys out and both said 1 downstairs 2 upstairs, 1 condensor. I’m near the NH boarder and sometimes I swear we are zone 4. I would never feel comfortable without a boiler.

I will try contacting some painters with old home experience.

Thank you!

Ditto what others have said about getting the right people to do the work.

Be clear with electrician that they are to minimize damage to plaster.

I've had a lot of luck using the old wire to pull into place new wire.

Holes for boxes can be cut with an oscillating saw and minimize damage.

Removing baseboards and channeling the plaster around the studs is a way to get wire across a wall without damaging the plaster or studs.

There are lots of tricks

Also, consider wireless light switches in some applications if it saves you from major plaster damage.

Minor plaster damage can be repaired with drywall tape and mud.

When I renovated my 1985 house, I had no problem cutting proper size holes in the plaster for boxes (switches, receptacles) and running wires from the basement (for the first floor) or the attic (for the second floor).

We have a 1897 victorian home, with some knob and Tube, plaster in various states and have added mini splits in some locations. Finding people comfortable working with plaster is the biggest issue we have had. There are people, but finding ones who are available right now has been a challenge. Before we have removed wallpaper we test walls by seeing how much "bounce" they have. Walls with lots of bounce likely have enough broken keys that sections of it are fully detatched from the lathe. These walls we have eventually taken down and then put drywall up place, mostly for expediency.

For our knob and tube we discontinued one loop for the top floor as part of other work. We were able to access and run all the new wiring through the attic flooring, so didn't have to do much that damaged walls. On our first floor we have been addressing abandoning the knob and tube, slowly when we are otherwise access inside those walls/ceilings.

I would think the electrician can minimize damage, especially if they are experienced working on old homes. We have had some remote controlled switches put in as well where there would have been lots of damage to wallpaper/walls in rooms. We had one room where there was no light switch, only a switch on the light, when we replaced the light we got a light that didn't have a pull chain, so we had a switch added in that room, which sends a signal to box the light is installed in controlling it turning on and off. We had this done as well to allow us to turn a stairwell light on and off from both the bottom of the stairs and the top. They have worked really well for the past year, and there was zero wall damage.

We also added mini splits this past spring, two on the main floor and one in an upstairs bedroom. In two of the locations (one on the main floor and the bedroom) we also removed the baseboard hot water radiators, as we were wanting those gone in those spaces to allow us to move walls. One of them is also in a room that still has baseboard heat, that one is mostly installed to give us AC throughout the main floor. WE LOVE THEM! Especially since it allows us to reduce room air conditiors but still have a comfortable home in the summer. They are so quiet! Despite being warned they are less efficient in the winter, they are still providing adequt heat where we need it. We had zero wall damange from that installation. One even when in a room that has wall paper.

Good luck!