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The shoulder joint is very complex. I wouldn't do anything, except under the guidance of a trained professional. It sounds like the professionals aren't entirely sure what your issue is or what the proper course will be.

If your shoulders are at the point, where every time you do X activity, you risk partial dislocation, then, at least until your get some great therapy, your going to have to change the way you do that activity.

One thing to look out for is that "pops" may not be dislocations. You could be dealing with tendons and/or ligaments getting stuck on and then sliding over bones, which can create a popping sensation within the joint.

My shoulders are also a major issue, but in terms of impingement. It just kind of sucks. I have to accept that I cannot do physical activities the way I want to. For me, my activity is bench press and weightlifting. Whenever I get my bench press close to a competitive level, I begin to get impingement issues in at least one shoulder. Once those start, it leads to inflammation and swelling, that makes things worse. I've accepted that it's just part of sports. Limitations come not only from ability (aka speed and strength) and drive, but also durability and ability to avoid injury.

I'm also somewhat lucky. Although my limitations prevent me from competing, I'm also not prone to any actual tears in the joint. So I avoid the need for surgery or limitations on day to day use.

You might not have to go as severe as "water jogging", but you are likely to have to modify the way you swim. I used to love to swim, but a perforated ear drum prevents me from going into pools now....

Edit: I would also try some physio and active rehab too, assuming your doctors okay it. A lot of shoulder issues are caused by the shoulder being pulled out its normal place by muscle imbalances, that can be caused over time by bad posture or too much computer use and/or sitting. This is considered "conservative treatment", and may be what the surgeon had in mind, when he said surgery was not appropriate. A lot of minor tears will also heal over time. The physio/rehab people can show you exercises to minimize scarring.