Well, that is a deep subject that has been attacked here from many directions over a long period of time. Reading related material here will help set perspective. Before commenting, here are some reference links.

https://www.tagengineering.ca/wp-content/uploads/2015/02/KVSApplDesign_catalog.pdf

https://bamasotan.us/range-exhaust-hood-faq/

https://www.houzz.com/discussions/2328297/range-hood-faq-personal-notes-updated-10-31-2007#n=20

https://www.houzz.com/discussions/2324336/vent-hoods-and-noise-the-real-scoop-on-vah

https://www.houzz.com/discussions/5161173/hood-faq#n=101

https://www.houzz.com/discussions/6099827/exhaust-hood-faq-ii#n=113

https://www.houzz.com/discussions/6040827/range-hood-noise-project

I think you will get a bit less high frequency blade tip turbulence noise with the blower outside, but without a silencer the difference will be small. A silencer could be installed in an exterior chase leading either to a "down-wall" (down-roof) blower such as Wolf and Broan make, or some type of down-blast or up-blast blower at the chase top. available from commercial ventilation suppliers, or an axial (Fantech) type in-line blower could be in the chase leading to some type of top or side cap.

Note that some die-hards have put chases inside bedrooms or bedroom closets to get the ducting to the aittic and roof. My attic is over my kitchen so I did not have to do that. I would, however for your case argue for any scheme allowing the silencer to be adopted.

Fantech and I think Broan/NuTone/Best have MUA systems that may work. More commercial units such as @opaone adopted -- Accurex I think; see his bamasotan link -- may also be available. The need for a blower enhanced ("active") MUA may not be needed if you have no combustion appliances taking air connected to the kitchen. This allows a "passive" (no blower) scheme to work if the duct is large enough.

Last, mostly for city apartments, there is the VaH ARS, which recirculates the air through a bank of filters. No MUA is needed with recirculation. Information on that can be found here:

https://www.houzz.com/discussions/2347276/vent-a-hood-ductless-ars-range-hood-update#n=181

@kaseki thank you for your reply! I'm not ignoring your message. I've read several of these docs, but not all of them. That's what I'm doing now.

It would be wonderful to build an external chase that goes up my outside wall to add the silencer and external blower. But that's _way_ out of budget. Not to mention the need to get in there to clean the silencer. So it sounds like a remote blower on the other side of the cooktop wall would be just as noisy as the internal blowers. Correct? So I think I'm stuck with the 1200CFM internal blowers on the Wolf.

I have sent an email to my city's building department asking if a permit is required, is MUA required, can I cut a 10" hole in my rimjoist for that MUA unit. We will see what they say.

As to the external 10" vent on the side of my house, I'm looking at this. I think this is designed in such a way as to allow the full flow of the 10" vent out. I'll want to mount this on a "mounting block". However, I can't find anything that's 14" square, so I'll have to make my own. I'm thinking PVC board that's somewhere around 7 5/8" wide. Get 4 of those and glue two together in one direction, then the other 2 in the other direction. Lots more to come. Once I get the hood ordered, I'll be creating a new thread on MUA. As a hint, I'm looking at the Fantech 1200CFM unit. There's really only one place in my basement that I can mount it, and that leads back to the "can I cut a 10" hole in my rimjoist???" Thanks for your response, Kaseki!

I don't think the silencer will need cleaning if the cooking is normal residential. In any case, if I were building a chase for the silencer and blower, I'd Tee into it and have a cover on the bottom of the Tee that I could pull for inspection and potential cleaning.

"Plywood" laminated structural members such as Microlam are available up to at least 16 inches x 1.75 inches thick. Having a short piece cut might be hard to get, but not impossible, I would think. Maybe a contractor who builds houses with large open areas would have suitable scrap.

Of course, there is 3/4 plywood that can be used if it will work for you, or two of them glued together (use Resorcinol glue, or one of the Pliobond or similar flooring adhesives).

Unless your house is similar to that below, you will need MUA for (a) allowing the hood to actually perform, (b) keeping down flow through cracks in the house walls, and (c) minimizing back-drafting of appliances. Even those on their own MUA may backdraft if you pull enough negative pressure in the house.