I'm not sure what you are asking about and it would depend on how big of a box you want but.......
I would cut two or three wedges out of 1-1/2" (or even 3/4") material and cut the inner part of the box out of them as close as possible and stack glue them to get the depth.
Keep the walls at least 1/4"+ thick. A lot of sanding (and or filing) will be required to get the inside a smooth as possible. Then glue on the bottom (same shape as the outside of the box) and sand the outside smooth.
The top can be done in the same manner only don't glue it on. You may have to use tape on two of the three sides while you sand one of the sides and then move the tape around to finish each side one at a time. I would use a slab of the inner cutout to locate the top by resawing one of the scrap pieces and gluing it to the inside of the top.
Glue the mouse on top and finish as desired.
If you have ever cut a bowl or vase, you will understand what I'm talking about and know that extensive sanding is just part of doing anything really cool.
Good luck and of course you need to post a picture of the finished box and, it wouldn't hurt to post some I.P. photos also! (In Progress)
Rog