You don’t have to be a male to go mano a mano—in fact, you don’t even have to be human.
The phrase “mano a mano” is, of course, not English at all. It’s Spanish, and its adoption by faddish catch-phrasers, particularly before the turn of the millennium, demonstrates a danger of borrowing foreign phrases into a language. For those who understand that “I’ll confront him mano a mano” does not mean “I’ll confront him man to man,” I give you a big hand. Or even a regular hand, whatever you like, and then you and I can go mano a mano.
In Spanish, mano means “hand.” Mano a mano means “hand to hand,” as in a style of combat engaged in primarily by males,
but certainly not necessarily so. The word traces back to Latin manus, “hand.”
On the other mano, if mano a mano were to be accepted by most English speakers as meaning “man to man,” then that’s what it means. Why shouldn't mano a mano join other now-acceptable English words that attribute their meanings to mistaken foreign borrowings (for example, cherry, page 149; crayfish, page 136; alligator, page 30)?
In a sense, we might say that we have been manipulated (worked by hand, not by man) into a manufactured (made by hand, not by man) English meaning.