If your shoulder is borked a lot of the powered options aren’t going to be a lot more fun to use than a hand saw.
Bow saws are a bit rubbish to be honest, a good, sharp panel saw (especially some of the newfangled ones that have a teflon-y coating) will usually work fine with thicker branches. I took a whole bunch of leylandi, broom and rowan down last week and just used my regular panel saw (not even all that sharp at the moment), cut through 3 and 4″ trunks and branches in no time.
Powered alternatives like a reciprocating saw are heavy (which your shoulder won’t like) and can judder about and kick quite a bit (which your shoulder won’t like either). You can’t really use them one handed either so if you’re lopping branches and the like you often need a second pair hands to support stuff or keep the cut open while you work.