First things first. I assume that you have seen a doctor and gone through some form of rehab on the wrist & neck. It does sound like you do have a pinched nerve in the neck/trap area, which in some cases may effect the wrist pain. Or even vice versa. Some of the Moto Cross, Quad and BMX riders I know try to shake off most injuries. Regret that after awhile but do not seem to mind walking with a limp for the rest of their lives. Off road and track bikes are very big out here in SoCal and anyone does not have to go far to be in the desert, mountains or find deep sand.
The BB BP, though a good exercise, is not alway the best for pec's. Do not know if you do this now, but try pushing up while the bar is resting on the heels of the hand. Will not stretch the palms and fingers back as far back as when doing a regular grip BP. The bar/weight in in direct line with the wrist it's self. Will need a good spotter if not use to this way of push pressing (this push style works great when doing military presses also). Putting stickem on the bar/heels of the hand can help with any slipping program. But the weight of the bar should hold it in place. Also change grip spacing when doing regular BP, like extra wide to the upper chest/neck. See if that relieves any wrist problem.
DB's would offer the best option for building pec mass, for most people. That and pec decks, where the resistance is on the elbows (superior leverage on the pec's themselves), not with the arms and hands way out away from the body. Cables are also goods, though the pecs lose a little with the direct leverage factor. Might try pre-exhaustion, with doing a set of pec decks (or cables) followed ,with no rest, a set of inclines or benches. You do not need extreme heavy weight to build any area of the body . Pure BB'ing does not really call for that. But you may need more direct time under tension (TUT) for potential muscle growth. Experienced BB'ers can make 10lbs feel like a 100 if they follow the correct workout plan.
I consider Dip's (weighted) as a better muscle builder for the whole chest area. But that is just my view. Change the grip/hand position around if you can. Knuckles forward or inverted, to a degree, if you have a "V" dipping bar. And if having a "V" bar than try extra wide to narrow and see what happens. Good Luck.
Side Bar: So true what you said about that smaller guy using 140's. See that all the time. But than again, do you want to be strong or look very strong. Perception is everything in BB'ing. Of course but for Colemen. Superior power and muscle mass, the best of both worlds.