No wheels, period. Let's keep that tiny percentage of forests as pristine as possible. No bicycles, no motorized vehicles, nada. If homo sapiens wishes to visit, it must do so like any other animal there, by its natural locomotion.
Bicycles damage paths and most importantly they ruin the outdoor experience for those that don't need contraptions to enjoy nature. 
Walking slowly along a quiet path and then, suddenly, "Bike on your left!" forcing you to jump out of the way--- no, not an enjoyable experience. 
Bikes and hikers are two different sets: let's leave in place the very few places needed separation can continue.