(And you ask about exterminating them. Did one cheat on you?)
Not knowing what a “Rat Zapper” is makes it hard to answer with any authority, but I am unaware of any truly painless rodent killing system. I trap them using a humane trap and then release them in a remote area. (Often my Mother-in-Law’s yard.)
A standard Victor mouse trap takes 14 ms to snap shut. (I’ve seen high speed videos – without mice) That’s about the same time as the reaction time of the mouse. If it is a clean hit, I’d say it is over just about the time they begin to enjoy the bait.