Was going to mention the electric fence charger, but thought better of it.
Do try the bucket with a couple inches of water. That works really good. You can even put a little wooden stick ramp up to the rim. They are not real bright they will fall in. If the water is deep enough, they can't jump out while standing in the water. Ive been known to put a teaspoon of peanut butter in the water and let it float around. Gets them every time.
The hazards of sticky traps:
If I put them where the cat can get to them, I put a shoe box or something over the trap. Cut a small hole in it on opposite ends so the mice can get inside, but the cat can't.
Like a roach motel. Mice check in, but they don't check out. Make sure to put the box along a wall. Mice will walk along the edge of a space before moving to the middle.
One more thing you can try. Sprinkle a little Cayenne pepper or other really hot ground chile powder around. They get it in their nose, and makes them starve because they can't find food. I usually sprinkle some in the corners where I would normally not go.