So what we need is a twin

So what we need is a twin study. "My brother Esau is an hairy man, but I am a smooth man."

You're committing the fallacy

You're committing the fallacy of cultural equivalence.

The cultures on the planet that have (and still do) practice depilation as a matter of course are in desert/tropical climates, where the main (acknowledged) reason for doing so was prevention of stale body odour. On top of that, the three religions in which corporeal hairlessness was/is seen as a sacrament are the (former) Azteca/Mayan religion(s), Islam and Judaism, all three of which were/are derived from civilised edicts for living in sweltering weather (with aboriginal records showing no exposure to lice pre-European contact.) Despite the contraindicatory nature of the practice (due to the potential for infection due to ingrown hair), there were plenty of non-Muslim African cultures which practiced depilation as well (and who, likewise, have no pre-European contact records of pubic lice.) On top of that, there are no non-European people on the planet who are especially hirsute. The few non-pale skinned people on this planet who developed "excessive" body hair have either a steady influx of European genes (due to cultural mixing) or had/have direct genetic links to the offshoot of the European fork of human diaspora (Hindus would be the largest example.) Seeing as how pubic lice require an abundance of hair in which to thrive, people(s) with limited or almost no body hair (whether through genetic structure or lack of nutrition) would have had a lessened ability to maintain and eventually transfer lice.