My idea was to make a humane mousetrap that would send a notification when it was triggered. This way, you don't have to check the trap, and if it catches a mouse, you can get rid of it quickly.

Step 1: Parts List

Swinging door type mousetrap. I like the Harris humane mouse trap:
https://amzn.to/2PytiVC
A wireless door sensor. I used an old Quirky Tripper, but you can get much longer battery life from a full sized unit. The Dome door sensor is only about $20, and works with Wink:
https://amzn.to/2Pyy2u5
Some strong double sided foam tape, which probably came with your door sensor.

Step 2: Remove Magnet

Take apart the magnet housing, and remove the magnet.

Step 3: Determine Where Your Magnetic Switch Sensor Is Located

Open up your door sensor, and look for a long slender component with a wire or solder lead coming out of each end. This is the magnetic reed switch.

Mark the location of the reed switch on the outside of the sensor body.

Step 4: Align the Sensor

Tape the magnet to the side of the trap door, near the top.

Locate the door sensor such that the magnet triggers the "closed" state reliably when the trap is set, and triggers the "open" state when the door is shut. Once you have a good location, tape the sensor to the side of the trap.

Step 5: Catch Mice... and Release Far Away!

Pair your sensor with your home automation hub or phone, and bait it with peanut butter.

When you catch a mouse, release it far from home. A CDC study found that mice could find their way back over fairly large distances. Release your mouse at least 2 miles away from home, preferably with some major physical barrier in between such as a freeway, swamp, lake, etc. (Source: https://wwwnc.cdc.gov/eid/article/5/1/99-0125_article)