Here's a picture of the second orchid in question. It wouldn't let me post multiple pictures.

To get multiple pics on one post try editing in word and then do a copy here. You have entered the terrarium world where you want dwarf orchids and the expertise to grow them. Is it worth all the trouble, worry and the expense of orchids when maybe other dwarf plants would be suitable.
Anyway, Den. Nora Tokunaga was bred by H & R Orchids in Hawaii using Species orchids from New Guinea, it might be easier to grow than the other Dendrobium which is a warm growing type of Dendrobium with at least one ancestor being Dendrobium phalaenopsis. Yes, you could lop the canes but the plant would be unlikely to flower because the flowering stem tends to come from the top of the cane.
Maybe you should divide Nora T. into two rather than into 4 or 5 cane divisions, if you did that you would not set the plant back too much but you should try and divide so that each division has multiple growing leads.
Hope this helps a little bit.

Thanks Arthur,

When splitting the Nora T. should I just divide the plant down the middle? Also, is there a preferable time to divide the plant? (when it's done blooming, after I've watered it, etc)

Thanks a lot for your advice

The best time to divide your plant depends on your growing conditions. Here, latitude 33S, I would never divide anything in late Autumn or winter.
No Climate details given but i read that the orchid mantis needs warmth. I only suggested dividing your plant into two because you are new to growing orchids and you might end up with multiple divisions if you do the usual thing and count back four or five growths from each growing lead.
So, the time to divide depends on your growing conditions, the type of orchid, the time of year etc. etc. For example, it is summer here and i am working through my Tolumnia collection, tidying up, dividing etc. because most have just finished blooming.
Be very wary, many people start off with that one orchid.....anyway good luck with the mantis.

My advice, NEVER divide any orchids!

It is extremely important for us to know what part of the globe you're growing on. Advice would be different in each case. For example, the picture shows bloom from the tip of the cane. This type of dendrobium as arthurm says is warm growing. The nobile types, which bloom up and down the cane, need a cooling down before blooming and then start to grow in the spring. That's when, in my part of the world, that I would divide and repot. And I would divide in half, no less, and use the tightest pot possible to accommodate the roots. But that advice may not be suitable for your part of the world.

I'd suggest taking your Orchids to someone who grows them and has experience with dividing Orchids - let them divide and/or prune them for you. They are too beautiful to butcher and kill!

So, how is the project going, or rather, how are the two projects going. You have probably realised by now that the orchid mantis doesn't need orchids. According to Doctor Google it will happy with any appropriately coloured flower, even plastic flowers.
You will be able to find complete culture notes for the pink (Phal. Type Dendrobium ) on the net. Not so for Den. Nora Tokunaga which as i said above is bred from New Guinea Ancestors and should not need quite as much warmth in winter.
I think the writer who said never divide any orchid was probably talking about the types with a single growth (monopodial) such as Vandas. You have to divide the other type (sympodial growth habit) once the plant becomes crammed in the pot with multiple growths or pot on to a larger pot.
Good Luck with both projects.