I think the closet door is a slider so a shoe holder would not work. There is a hook inside the bathroom door that may be a possibility for you.
Other than that, what about just picking up those hooks with the magic strip on the back. Inexpensive. You can use either the lock off door or outside the bathroom door. Remove it when you leave and it does not leave any marks or damage. They sell larger hooks for heavier items. Don't know the weight limit on them though.
Or get a shoe holder that can be used on a hanger and leave that in the closet.