Given a greater degree of reproductive success for females than for males, it may follow that more transvestites would be male. Are there any data? Are the males (who tend to be more territorial in obvious kinds of ways) making a more conspicuous display and getting more resources in terms of social power?
Male plummage: Zahavi hypothesis (in Ridley, Red Queen: Sex & the Evolution of Human Nature, Penguin, 1993, pp148-149) The larger the display in peacocks, the more hardy they must be to survive. Zahavi was initially discounted but is taken more seriously in the past few years. Is there a remote implication that lavish transvestism is a form of male competition that takes advantage of female scarcity?
There may be other species where the male exaggerates his female characteristics. Gould & Gould (Sexual selection: Mate choice & courtship in nature, NY: American Scientific Library, 1997) Male hangingflies (p 215) pose as female and steal courtship gifts, intended for females, from other males. Some male gartersnakes emit odors of fertile females and elicit copulations from other males, inciting them to waste resources before the imposter slithers off.
Wilson, E.O. Sociobiology (Abridged) p 163 re AJ Bateman Principle concerning differential reproductive success for females and males. Explores the relationship of that difference to parental investment as a function of gamete scarcity. The scarcer the egg, the more the parental investment, and the greater the sexual selectivity. Thus females tend to be more choosy about mates than males are; males attempt to fertilize as many females as possible. The girls, in many species, apparently get a lot more attention then the guys.