I should point out that there is a cocking devise that enables one to shoot a vert like a crossbow. In fact I saw a vidio of a person with one arm using it. Do a search.
X bows are not quiet as a rule, not like a vert. You will experience what sound like a lot of noise the fist time you shoot one. There isn't much you can do about that. Speed of bolt compensates somewhat but not for shots past 35 yards or so. To get over 300 fps you're looking at a bow that has a pull weight of 150 lbs (compound) and 200 for a recurve. Given your shoulder (I have same issue) you'll need a cocking aid, at least initially. You may also consider the prospect that you won't be able to pull a vert repeatedly after the operation, making practice and shots more difficult. (Happened too me). So buy a quality bow. You can sell it for llittle loss if things work out as planned.
Regardless if this temporary or not, I'd look at a qaulity bow (Exca, Parker, Ten Point). Excal is simpler to maintain but bigger overall. How you hunt may determine your choice. The compounts are smaller overall so handier in a stand or blind. And shoot as many as you can before you buy to determine how they fit you and the quailty of their trigger. IMO a smooth and predictable trigger release is most important to good accuracy.
But your expectations fo shooting beyond 40 yards may be problematic. I realze that some vert shooters are now shooting out to 70 yards. Personally, I have more respect for game.