There is nothing wrong with this; it's a good example of matching possessives when the owner/object's genders are in opposition.

Tricky! I misread it as "shirt" for obvious reasons. That Duo- always trying to put one over on us. Actually, I can imagine a few recent sentences together in one story..."I don't dress women" "his skirt".....I'm imagining a story that revolves around a gay guy working with models in a fashion show :)