Speck, I don't think it matters what styles society defines as being appropriate for women to wear, no matter what culture, what century, how frilly, how plain, how long, or how short. Most CDs would want to wear them too, whether the motive is to emulate a woman or be a woman.

If we lived in a world where men wore only dresses & skirts and women wore only pants, CDs would want to wear pants too.

As to the burqa, in the Middle East I should think it would be necessary for a CD to wear one in public in order to be sure that any hint of his gender were well hidden, else the consequences would be dire. I'm guessing that in private he'd wear what women wear under their burqas.