How do you tell one from the other? If he actually identifies as a woman, what's the moustache about?
If I got caught skulking around in a lady's restroom, claiming that I'm trans would be my go-to response. Might even buy me enough time to get away before any consequences.
An an aside, do you have any data to support that factual claim?
The only way you can tell what gender a person identifes with is to ask them. You can make a guess at that by their appearance. Both genders have facial hair. Some women have mustaches, but most of those remove them.
I would never be "sulking around" in a lady's restroom. I might go in one to relieve myself if the men's restroom was closed, but I would do what I had to do quickly and leave ASAP.
I didn't have any data to support my claim that 99.9% of rapes were done my straight males, but I did not look in up on the WWW, and found that 93.6% of sexual assaults were done by males, and hetrosexual men are responsible for the "majority" of sexual assults. So, my claim of 99.9% was an overstatement, but the data online, although not conclusive, would support maybe an 80% claim.
Quick Facts on Sexual Abuse Offenses (ussc.gov)
Statistics In-Depth | National Sexual Violence Resource Center (NSVRC)