Interesting question. How about motorcycles, bicycles, roller skates, etc. ?
I'm guessing the 'in' the automobile or other private form of conveyance might be the key. (auto, truck, airplane, helicopter, etc.). You wouldn't actually be carrying the gun 'in' a wheel chair, bike , motorcyle, skates etc., you would be carrying on your person while riding those things.... I suppose maybe if on a motorcycle you had saddlebags or those storage compartments it might count as 'in' the bike.
Good question to ask an attorney your attorney general, then you could let us know what they say.
If it were me, I would get the CCW permit, because even if it is ok to carry in the wheelchair when you're being conveyed from one place to another,
it may be a different story when you stop at a restaurant or something and your wheelchair becomes a seat rather than a form of conveyance.