Oh, sorry to hear you need surgery. Hope you have a speedy recovery.
How is your dog on lead now? Pulls? Heels nicely? Will he/she try to bolt to end of lead after a squirrel or anything like that?
If it was my neck and shoulder, and there was ANY chance that my dog would pull for any reason, I'd probably use a short traffic lead in my good hand and a prong, to minimize the chances I would get jerked or pulled off my feet feet during recovery. Or, if it is in the budget, hire a dog walker or get a friend to do it for you until it is safe.
Even if your dog is 100% on lead you have to allow for something off happening, like a row with an unleashed strange dog. if something like that happened, I would not want to be tethered to the dog. Being able to drop the lead quickly would, unfortunately, be the safest option.
I agree with comet depends how much your dog pulls. Gandalf doesn't pull so I actually just take our bungee leash and put a carabiner through the hand loop and clip it to a loop on my jeans, it does the trick!