Sliding doesn't affect the hitbox of your mouse. You can simply run under the fan, and if you're lucky, you won't be blasted off to your death. If you want to be the first mouse to get in the hole, using this strategy can be useful, though you still have a high chance of dying.
Either use the strategy as explained above, or wait for the shaman to help you.
The map was designed with trampolines in mind. The fan is supposed to be an obstacle that instantly kills any mouse touching it, and the shaman is supposed to place a trampoline on both sides of the fan so that the mice can jump on it in order to get over the fan.
Due to a glitch, you can place a box or a companion crate which stands on the ground, but touches the fan, in order to stop the fan. This won't always work. Be sure to have the box or companion crate touch the ground.
A former method for more experienced shamans can "spirit it away", by continuously spiriting the red nail until the plank glitches and gets stuck in the top left corner. Though after performing this glitch, it is not recommended to build red nails because those will be stuck in the same corner as the fan.
This glitch was later patched in an unknown game patch.