Do I look like a vet to you? :roll: :lol: .
I have no idea how to try it. I thought perhaps it might feel obvious once you wiggled it. Whether or not you hurt him is a moot point since I am sure he is not comfortable as he is and won't survive without intervention since he can't eat. Putting dislocated bits back in humans hurts, and so does the dislocation itself, so don't think about the pain you may cause, just hope you can get his mouth to shut again.
If you can't see the jaw is obviously out to one side or the other that leaves moving it forwards, or backwards.
Good luck. Rather you than me! 8)