Any motor that's covered by the controller can be used to even power the go kart.. you'd need to adjust the gearing to compensate for the additional weight compared to a wheelchair (thus you'd end up with less speed)
same goes for the steering, if the controller in question was meant for low speed small wheel steering, you'll likely need to add some oomph to reliably steer a gokart (especially if it's not a road kart but meant for some light offroading [aka back yard fun

])
I'm sure you'll have dozens of questions, but asking about the wheels now is a bit premature..
as long as you do not know how to even power the kart for your son, not to mention steering it.. the color isn't too important, is it

Rims depend on the tyres you want/need...
Personally I'd say it might even be worth looking at a gasoline engine instead of a DC motor.
that way you have all the forward momentum you'll need for sure;
Simplified down:
In the end, you'll be building a pimped up wheelchair with a wider track and a longer wheelbase.
If you keep the wheel diameter and the overall weight somewhat identical to the original wheelchair you'll be good with all the motors and controllers you currently have on said wheelchair.
if you increase wheels or weight you need to gear down (slower) or have a more powerfull motor.
But how about that:
tell us what you have in mind more exactly
race kart [unsuspended, small wheels with slicks],
yard kart [unsuspended, slightly bigger wheels with knobbies, a brush guard],
buggy [suspension, big wheels, a serious rollcage]..
something inbetween...?
And if possible show us what you have to work with (the controller, the motors etc.)
that gives us a better idea where to start.
Maybe what speeds you'd like, if you want/need something I cannot think of at the moment (like some sort of additional medical equipment or a remote control or something)
The more info we have to work with the easier it'll be to help
'sid