Basically, the cheese paper maintains humidity but allows gas exchange, allowing the molds (or in the case of the stinkies, the BL bacteria) to continue to do their thing. I've not made a stinky cheese (yet), but based on my experience making quite a few camembert styles, I would say that it will be fine to keep them in the ripening box - I've made them both ways, and both work well. The paper is just more convenient.