Try putting the shoe box in the a lower cabinet with the door just ajar keeps the dogs and cats away). I used a similar technique using 3-4 traps lined up in the box. mouse had to climb on a trap just to get anywhere in the box. I didn't use cheese (never works for me). Mice love peanut butter and grass seed. I put the peanut butter in the trap and sprinkled grass seed all around the inside of the box/on the traps. My record was 5 mice in one day using this method (in my garage).
If you have to have the trap box out in the open you could try heavy duty double sided tape (like carpet tape) to stick it to the floor. Then you would just have to use "leave it" for the dogs.