Mice can not do anything without the shaman's aid.
It is nice to note, though, that it is possible to mid air jump from the top part of the map back to the bottom part (this may require a wall jump though) without the shaman's assistance.
Build a ramp around the platform. Be careful not to trap mice, since most times you'll have to build slightly around yourself. Make a platform with at least three rows of conjurations until all mice have gotten to the cheese, then build back. Most mice will Air Jump back to the hole. Also, you can glitch yourself through the roof above you, and then back down once you've gotten the cheese by trapping yourself with conjuration and putting conjuration behind you.