So as far as I can see in the rules Natural Armor doesn't specify if it's soft or hard armor for purposes for things that reduce armor such as Hakyoukuken. Me and my group just ran into this problem for the first time and I would like some input from people who also have run into this situation.

If you are referring to the advantage made for playable characters, I think it should be considered as soft armor (since skin, even when really thick, is soft and elastic). Concerning the natural armor of chapter 26 (creatures' creation), my opinion is that this is up to the GM to decide in regard of the created creature.