Mice can not do anything without the shaman's aid.
The only useful method is to build a ramp up to the cheese. Due to the nature of Conjuration, it is impossible to build anything else. Point an arrow to yourself. Then, when mice stand with you, start with the conjuration directly beneath you and move the mouse straight up. The conjuration will push you and the other mice up to the cheese. Then you can jump down to the hole.