Bolt a holster to his chair frame, he can either reholster or place the gun in his lap while moving between positions.
If it has to be concealed he can toss a blanket over it and his lap, pretending to be a poor defenseless cripple.
If needed he can be pushed between stages or shooting positions, face it, he'll never take out a championship so why worry about the fine points?
Set up stages with prone or a low port so he can shoot around the obstacle to the side, set the ports at 'squat height' so he can shoot through them. If he can exit his chair, make prone the last shooting position. Be creative with stage design.
We had this discussion in Australia in our IPSC forum, as I had a wheelchair member joining. After due discussion with the international secretary, myself as the section secretary, the NROI chief and our national legal counsel, it was decided that he would be allowed to shoot in whatever way he could and that anyone who objected would be beaten up and thrown off of the range.
BTW, my wheelie mate hoons around in a V8 street car, gets to shoot MP5s as a prison guard, and is a military rifle shooter as well, when he's finished with prone we help him up again. His legs don't want to work, but his heart makes up for the rest of it.