How bad is the soreness? I also wouldn't have thought it would prevent an operation. How often do you change the bag? I've always had really good skin, and I think this may at least partly down to the fact that I change my bag every day, as this allows me to thoroughly clean and dry the skin every day, rather than letting it sit mucky for days.
Also try using an adhesive remover when you take the bag off. Since the soreness is where it's sticking to the skin, maybe you are taking some of the skin off when you pull the bag off.
Have you asked a stoma nurse about it? There are all sorts of creams available for skin care. Also if the problem may be a result of the skin not being properly dry, there are powders you can put on to help with this. I always put a lot of powder on. Finally, since you mention lack of air, have you tried taking a bath or shower with the bag off? My stoma is fairly predictable in when it works, and often goes long stretches without producing any output, so I can leave the bag off for a while without too much worry. If you leave it off in the bath or shower, if it does start producing, the mess will be easy to clean up.