I have recorded an instructional video for disabled people with a Rode Nt4 some time ago.
I suggest you to pre-observe the operation of a wheel chair before recording it. With observation you can decide easily about your recording techniques.
Wheel chairs are not noisy and squeeky unless they are very old or some mechanicals parts are rusty. I recorded the friction of rubber wheels on different kinds of surfaces (wood, stone, etc.) Because when they want to turn left or right they turn on the wheels. Watch paralympic basketball from YouTube and you will see what I mean.
There are also some mechanisms to stabilize the wheel chair when the person wants to stop. This locks the wheels and you might want to record these kinds of "click" sounds where two metal parts gently hit each other.