silly word games

"Per-offspring," not "per-son."

You don't want to keep the 'wo-': its root was 'wif', thus defining a woman with reference to the man who was her husband. (English is weird, one of very few Indo-European languages whose word for 'woman' does not derive from PIE *gʷḗn, though obviously that is still around as a term for one woman in particular. Or, at least, one woman at a time. Note: the female name 'Gwen' is probably unrelated.)