Cute idea. BUT. There is a lot to be considered. Time limit will definitely be a major factor in this. If you can't change your costume in less than 10 seconds, I would consider doing something else. Count it out for yourself. 10 seconds is an eternity on stage.
If you can change that quickly, great. Moving on. Is a screen necessary? Is there an artful way you can change or is it going to involve a bit of unsightly twisting and pulling? Being able to change gracefully in front of the audience is far more interesting to them than a blank screen since they're then involved in the transformation, even if you have a couple of invisible helpers. Doing it that way would also mean that you could take more time to make the change.
Hope this helps! Let's just say I'm used to taking things off on stage.