I’ve spent WAAAAY too much time thinking about this problem.  Here’s my new idea:

• Print two mouse funnel mousetraps.
• Drill a 4cm hole in a door along with 4x 3mm holes
• Install one mouse funnel mousetraps at the bottom of that door, with the pointy bits facing outside
• Put a box with peanut butter in it on the other side of that door
• Put the second mouse funnel mousetraps in the box, with the  pointy bits facing outside

The hope is that a mouse inside your house will walk out the hole in the door to get to the peanut butter on the other side of the funnel.  Once inside the box with all of the peanut butter consumed the mouse can either (a) try to struggle past the pointy bits back into the house or (b) slip outside through the second funnel.