Jump while you walk to move faster on the sticky ground. After reaching the pillar, Wall Jump on it and pass it. Walljumping is easier here, because of the stickiness. After grabbing the cheese, the only way to move is by jumping and walking, as the cheese makes you too heavy to move on the sticky floor.
The shaman is pretty useless here, but he can build a ramp or an air ship to help players who can't walljump. If you are going to build ramps then start on the far side first to give the mice a chance to walljump if they desire to. Attaching a free anchor on the near side will make sure any failed walljumpers will not become stuck. The shaman can place large wood planks on the chocolate floor to help mice run faster, especially after getting the cheese.