Those definitely exist, Dixie gunworks used to sell something like that.
I've managed to take out 16 mice from under my front porch, some were shot others were trapped, but there's two big ones that seem to be too smart to come out when I'm there, and smart enough to avoid traps.
I've considered making something akin to that using a camera and remote "detonator". Stick it under the porch, and when the camera senses motion in front of the barrel, it would trigger the shot. That way the mouse wouldn't have to actually step on a trap, all he has to do is cross a line.