Congratulations and welcome to the club. I tore my right rotator cuff last year and doc says it won't heal, ever, even with physical therapy. It keeps me awake at night, but I'm learning to live with it during the day. Key is to isolate that joint as much as possible, keep the elbow against my body when I'm lifting anything. Doc says I can do anything I want with the shoulder as long as it does not hurt. If it hurts, stop doing it. I got in a lot of days on doves this past season, starting with an 1100 .410, working up to an SX3 20ga with a couple of featherlight loads, then to my 686 20ga with Walmart promo loads. That's the point at which the shoulder began to talk back to me. I shot a few pheasants with an SX3 20ga and 3" Black Cloud, and that was OK for the number of shots I needed. Tried some 2-3/4" and 3" duck loads in an SX3 12 ga, and it was tolerable. Your Citori might be OK with 1-1/8oz loads instead of 1-1/4oz, but I bought the SX3s just so I'd have a couple of soft shooting guns that could take steel. I'm backing off on both velocity and shot charge, and got the gas guns just to protect the shoulder until I get the surgery.
Re risk of RC surgery, my doc says it's outpatient, arthroscopic, minimal risk. He won't really know about the specific repair or recovery until he gets in there, but warned me that recovery could be 6-8 months with lots of PT. The caution is that I have an 80% tear, and if I tear what's left then repair success can be iffy. Have you had an MRI? How severe is the tear? My doc says that if the tear is complete and not repaired fairly soon after the separation, the tendon retracts into upper arm and he may not be able to pull it back into place and re-attach it. If you have not had an MRI, get one so you know what you are dealing with.