Our jaw asymmetry is pretty similar, and I have the same dilemma... fix the teeth and leave the jaw, or fix both? One of the main reasons I wanted braces was to fix my jaw, and then I found out braces alone wouldn't take care of it. I'm in braces now and debating surgery, but leaning towards it.
It sounds like the physical appearance of your jaw bothers you. Do you think you'll be happy with the outcome of the braces only option?