"The word, "nanny" generally refers to a female caretaker, other than the mother - the idea of maternity or maternalism; feminine characteristics (which are oft thought of in partnership with children and childbearing). The term, "cock" often is used in reference to the male chicken or as a common suffix to a male personal title. Given these two ideas, I see them to be a self-contradiction when combined.
Along those lines, it could possibly mean "a man who raises a child single-handedly," or one who chooses to, at least. I also believe it could either mean an "effeminate male," or perhaps a transvestite. I do not know how prevalent transvestitism actually was a century or more ago, but I would assume it was not extremely common. If that is the case, it could be argued that the rarity of the term fits the rarity of the practice, making the proposed definition a likely candidate also."