Tranvestite's Style

James Caan did win that fight because he got the last punch in. But when I first saw that scene I thought "Bruce Lee in drag!"

In 1974, he would still be a transvestite, or perhaps a cross-dresser. It appeared to be more a situation of opportunity (robbery) than any take on society's gender roles (even though he was gay). And don't transgender people dislike the "ed" in "transgendered"?

Not at all. He was a crossdresser, strictly speaking, as we have no clue he did that for sexual pleasure.
However, in the tub scene, he talks like a gay, so we can assume he's a transvestite too.
Crossdresser = wearing opposites'sex clothes for no "weird" reasons (ie: Halloween make up, a joke, creative dressing style).
Transvestite = wearing opposites'sex clothes for "weird" reasons (ie: sexual pleasure, prostitution, gender disphoria).

'What has been affirmed without proof can also be denied without proof.' (Euclid)

Christopher Morley is credited in this film as "Transvestite," regardless of whatever picky language everyone wants to label themselves with today.