A cat's out of the question. My daughter has a Schipperke, but the problem is, she can't get into the tight places a mouse can get into.
Watch the video to the end and you'll see I finally caught it by using an old-fashioned Victor trap with the metal bait-holder. Even so, he almost eluded the trap and ended up getting caught by the snout and suffocating to death.
Peanut butter under the metal bait trip and two traps facing or perpendicular to each other, (double kill sometimes) the mouse will bump one while trying to get the other. Mouse trapping super-hero here (at least to my wife). :)
Full disclosure: I did not watch the video. That being said, I had a couple (ended up being 3) in the house a couple of weeks ago. My dad bought the awful snap traps that have the plastic part that looks like cheese - they set those traps off pretty much every time & do not get caught.
I watched a video by someone who says he can increase to about 90% the odds of catching one in a snap trap - he likes the Victor brand so you were ‘doing good’ on that part. Then, he takes a small pretzel & hot glues it to the bait plate/holder. The mice grab the pretzel & it sets off the trap. Using peanut butter generally does not work because they can lick it off without getting caught. One trick with peanut butter is to put it on the bottom of the metal bait plate/holder.
As for me, I put PB on the “cheese” bait plate, then smushed a peace of cracker down on it to keep them from licking the PB - caught one mouse that way; however, I had 3 traps sprung & no mouse caught with the same setup. I caught the other two in glue traps - I know ... cringe ... I hate them, but they work better for me than snap traps. I put a tiny dab of PB in the middle of the trap & they go for it. I watch the traps carefully & dispatch the mice quickly so they don’t suffer any longer than necessary. With the glue traps, we caught one within an hour of my dad seeing it run across the den & into his bathroom ... we caught the other in the early evening after noticing a partially eaten avocado on the counter in the morning. That mouse got on the trap while the kitchen lights were on & my mom was actually in the kitchen! Bold mice! We haven’t caught any more and I’ve had traps set in 3 places.