Do you have your own computer near the desk you work in your cube? One possibility is to rinse your clothe and place them loose in a fishnet bag with a dry towel to catch the water drip. Then place the bag behind your computer as discretely as possible. The heat from the computer will help air them out and expedite the drying process. If you are worry about any odor, you can place a 1/2 sheet of Bounce Fabric softener with the clothe to cut down the odor.