Would you like to borrow a terrier for a night? I guarantee you, no mouse tomorrow.

Humane (live) traps work well. My problem with the snap (dead) traps is that sometimes they don't work like they are supposed to. I don't really have a problem with a fast, immediate death. But sometimes snap traps don't kill the mouse immediately, they might just catch it by it's legs, or even break it's back but not kill it. That is VERY hard to deal with.

I hope your cat didn't injure the mouse such that it crawls away somewhere in your house and dies. Not to be gross, but if you don't catch it soon, you might want to start sniffing for bad odors.