All it says in the rulebook about stunned players is:
It does not specify what action the player needs to take.All they may do for their next action is turn face up.
LRB page 12
So i would declare a blockaction with my stunned wild animal and turn him face up without rolling a die.
You may not stand up during a blockaction (LRB page 12), but is rolling over to the other side considered moving somewhere?
This is worth considering with the new wild animal rule