Most of these old EM shooters' guns were made from real guns. If you can't find a replacement you could match up the existing one and make your own. I'm sure if you dug deep enough you could find an original replacement though. Does the game work?
Well, I'm not 100% sure what brand of gun goes on that game. I have 3 EM shooters, my Captain Kid gun and Arctic Gun both use actual Remington .22 rifles. The ones on Twin Skeet are obviously shotguns; I'm sure you could replace it easily enough. You could also put up a WTB ad right here and see if anything pops up. Its always surprising what people have for parts; and they're willing to sell. Check out these links: