stuck -like the stones are Stuck in the pouch or tubes that go into the pouch?
As a medical professional I know of different options, but I see no reason to recommend them without a good reason. Why don’t you want to have the gallbladder removed laprascopically? It can be done as an outpatient in most cases. You need to have G.A. (knocked out), but that’s no big deal. Once it’s removed you usually don’t have any problems in life from this.