The bicycle wheel wont work. Because of the center mounted hub it will be the wrong shape ie not flat if the spokes are left on and you would need a cup shaped piece to go over the hub. If you remove the spokes and centre hub there is nothing to attach the chair to at the center.
Ok, I guess you could make it work but it would be a lot more effort than car tyre rims or hubcaps.
Hey boomer, have you seen these?
