You are going to need the deflection choke. How else do you plan to move the beam? Unless you have other plans to deflect the beam? If you remove the choke then you won't need the vertical osc. You will need the horizontal osc as I recall it drives the HV for the tube. You won't need the video or audio amp. You won't need the tuner.

If I recall correctly, some of those chokes were bonded to the TV tube. I could be remembering that incorrectly. If that is indeed true then I suspect it was to reduce alignment issues.

Remember you will have 3 guns on the tube to control (red green blue). You will be really lucky if you find an old B/W that still works and does not have the phosphorous screen coating all burned..

 

You can take the deflection yoke off of the CRT but you need to keep them connected to the chassis to act as inductors so the high voltage will still be made and scan failure protection (where present) does not keep the beam cutoff. Some monitors do not require the vertical winding for your project and some do. There are a few high-end monitors that have separate high voltage power supplies, but they are probably very scarce now.

CRT computer monitors are simpler than TV sets and probably easier to work with.