Looks like part of your problem is solved. I worked in a cubicle years ago, and used one of those "over-the-door" devices with a row of four clothes hooks. The squared-off tops are meant for hooking over doors, but they also worked on a cubicle partition.

One more tip - a spray bottle of Febreze in that deep desk drawer. A quick spritz on the sweaty part of your clothes right when you take them off will keep bacteria from creating the odor that most people mistakenly think is the smell of perspiration. You can use the stuff diluted to at least 50-50 with water. If you hang your clothes is a closet, the other user(s) of that space will definitely appreciate the difference, and you'll find them much more pleasant to put back on at the end of the day.