I had a pretty bad shoulder strain many years ago (dragonboat racing) and was still able to ride a mountain bike, but did not venture off road very much. I couldn't afford my own bike, so I borrowed from friends, and the bikes were typically a bit large for me. So between the long reach and wanting to take care of my shoulder, I relied a LOT on core strength to be able to handle the bike.

I should note that I was in constant pain at the time, cycling didn't hurt as much as other activities, and I had yet to learn to really listen to my body when it was injured.

There are some threads on here about recumbent bikes that would probably be worth reading. Could be a good option if you are looking at a long recovery.

Every body and every injury is different. It might be worth getting on a stationary bike or a bike on a trainer first to see how confident you feel with the shoulder, before taking a bike out on the road or trail.