You cannot complete this level without the help of the shaman.
The shaman will need to build a ramp or staircase to the cheese. Airships are not recommended due to their instability. Some mice build a supported platform to the right, with a trampoline at the end. Though lacking in creativity, most mice are able to get cheese without problems. Supports can be added by either creating a small board with a world anchor underneath the bridge, or by attaching a ghost board with a world anchor to the bridge. A fun idea to try is to use c nails to create a bridge of long planks without supports, and use a ghost down canon on it to create a diving board.