When I worked TSA any black powder/ substitute was considered hazmat and the caps #11, Musket or 209 were also hazmat. Just declare the gun and if you don't mind loosing the powder and caps you can try it. You may not have someone who is as familiar with muzzleloader and what is hazmat.
I would just by the caps and powder down there, but due to the size of the animals the 50 cal may blow away half of it.
Good luck are you by any chance going to FLETC?