OK, I did some brainstorming and came up with an idea. If I held the jaw in position and drilled through the skull and jaw where they connected with a 1/16" drill bit, I could use a 1/16 Allen wrench and maybe a little silicone to hold the jaw in place. If I didn't like how it came out, I could change the position and re-drill using the original holes in the skull so that the jaw would have a couple different sets of holes for different possible positions. This is what I have done so far. I used drill bits as I'm waiting on the cheap Allen wrenches I ordered from Amazon:
I picked it up and held it from the skull portion and the jaw stayed. I haven't added silicone yet as I will do this with the Allen wrenches. I will likely paint the Allen wrenches white and cut them to the desired length so they are less noticeable.
Since this was an experiment, I used an old javelina skull that I didn't take care of just in case. What do y'all think?