It is possible to corner jump from either the platform you start on, or the hole platform, off of the lower platform, grab the cheese, and make it to the other side where you Walljump to safety, but it is extremely risky. Under most cases, it is better to wait for the shaman to build to the cheese.
There are a couple ways of getting the cheese, but the most common is a bridge down to it. If you have skills, you can put a spring or cloud under the cheese to help the mice get it, but that requires a decent amount of shaman level. As this is a shaman duel, be aware that the hole you control is the hole opposite of the side you spawn!