In my opinion, I would say have your vet do it. Shooting is just too inaccurate in my opinion. Both can go wrong, but from my experiance the injection is less painful and less traumatizing for you as the owner. (I'm speaking of regular guns, not captive-bolt which when done correctly is deemed humane.) Lethal injection, from my understanding, is an overdose of a general anesthetic which causes the horse to fall asleep as if going under for surgery and then because of the overdose their heart stops. I think that sounds like the best way to do it.
(And as nickelodeon said, do it in two doeses, not just one)