Ross, this is all I could come up with, but it may not be the same on the larger wheels.
The smaller 12"
(PW-12H) wheels have an 18mm diameter shaft which uses a 4mm key to transmit the torque from the axle to the mounting bracket:
Unfortunately I don't know what size or type of fixings are used on the larger 24" diameter wheels like these:
I don't suppose Gary actually got to see what type of axle fixings were employed on this particular wheelchair, as I suspect it might have been shipped direct from China.
Alan