Map 96 consists of many pieces of dynamic ground stacked up like a pancake. They will easily fall down if the shaman doesn't prevent it.
Don't try to get the cheese on your own: You either won't get it and return to the platform or you will get it, but then fall off. Maybe the dynamic wood can be reached then, but it is almost impossible to walljump the stack. Wait for the shaman to do something, then get the cheese when it's safe.
First, attach the upper piece of dynamic wood with a red anchor.
In hard mode, use your totem (if it doesn't have a red anchor try to stabilize the pancakes by putting anvils onto them - that will be difficult though). Furthermore you can attach the two or three pancakes under the first one too to make the map become even more safe.
Then attach a long solid-anchored plank to the right of the stack in order to make mice reach the cheese. It's not required, but recommended to to so for the right of the stack, too, because some mice won't reach the hole and fall off then. If you are going to do so, attach the right plank first, then the left one.