I don't know as I've never had a mouse problem that I know of, but I do know that were I in the market for advice about how to catch mice, the guy named Owl would be the one I would listen to.
Having said that, starving your cats would be mean. Have you seen these new mousetraps where you never have to see or touch the dead mouse? You twist it and put in some peanut butter to set it, then they go into the trap, and it snaps untwisted to decapitate the mouse and close it up inside the trap. I was like "This is a symptom of our culture which hides from the messy realities of life THAT IS SO COOL!"