...at least until next week.

This may be well known, but was unkown to me. If you're wearing an exotic cloak and swap allegiance to another faction, it will disable the cloak. You lose the perks and light from your cloak while it is equipped. I swapped to another cloak and can't equip the exotic one until the weekly reset.

Anyway, if you want to do the no-cloak hunter look, this is one way to do it.