If someone gives you a firm pat on the shoulder is that aproblem? If not you will probably be fine with a 22 as the recoil is less.
No one ever thinks about it, but if you needed to you could add a decent recoil pad. With a heavy semi-auto 22 and a $15 recoil pad installed I can't imagine you would have any trouble if you can fire pistols. In fact, if you are firing centerfire pistols you are probably good to go.
Talk to your doctor, but he may say no simply b/c he has never fired a 22 and doesn't know what the recoil force isn't.