I'd still call your doctor and ask their opinion. I'm betting that they might advise against it, you know docs and liability. But, if I were in the same position, really wanted it and was in good health, I'd probably go ahead and do it.
My wife's an RN and I just asked her. She said that she wouldn't think it would be a problem as long as you keep any appendectomy incision bandaged and clean your tattoo as recommended.