If it doesn't actually provide a method of calculating your AC (i.e., is not an actual armour, in this case), then by rights it should not require armour proficiency to use. You could take a look at, say, the Helm of Brilliance, or the Helm of Telepathy as examples of helmets that are pretty darn distracting and cumbersome, but which nevertheless do not impede cloth-wearers.
That said, Crit Protection is a pretty strong perk to have on a functionally mundane item.
