It's not your arms really, it's your back. Your arms just have to hold the gun isometrically, on a pistol, you'll use more arm muscles, as there's no stock to brace it to your back. So for pistol shooting, you'd probably be able to have direct forearm work (either a gripper or hand roller) help you a lot, but for a rifle, I don't know how much that'd help you, unless you're having trouble just gripping the gun. For a rifle, you'd probably need to do some compound exercises that involve your lower back and legs, so odd as this is to say, probably deadlifts would be good for you. Deadlifts are just when you pick up something off the ground and get it all the way up, with no arm bend, though. Deadlifts very much improve grip strength, as that's half the battle in getting the bar up, gripping it. But mostly, they work your lower back and legs very well, so you'll be able to be more stable. http://www.youtube.com/watch?v=5M13EBl_jF0 Very good example of a deadlift.
Obviously too, you do know why the Army does pullups, pushups, and situps, right? Pullups and situps very much work the back and core muscles, and then pushups work the arms but moreso work the upper back and shoulder muscles. So there's always those, too. You could also look into standing overhead presses, ie, standing, with your legs straight, you press the bar up over your head until lockout. It was actually called the "military press" as the military used it to measure strength until I think the 70s or 80s or so. It was sort of "the king of lifts" if you would, until the benchpress came along. http://www.youtube.com/watch?v=xDulY9AJc_c Example of overhead presses. I think the reason it got less popular is, it's easy to hurt your back if you're an idiot, and also in the Olympics, people would really hyperextend their back to press more weight, so that made the lift harder to judge but also more dangerous, so yeah.
That's just my input, though. See what works I guess.