I would assert that any derisive couplets about the captain's daughter are of modern origin, not traditional.

You cannot convince me that any chantyman with normal survival instincts would have made disparaging remarks about an officer's wife or daughter at deck-level (where "Drunken Sailor" would have been used). In that era, such utterances were "fighting words" of the first order. And ship's officers could make a sailor's life miserable or end it entirely. To insult an officer, or worse yet, his wife or daughter in his hearing was inadvisable.

Now it was traditional to say some things about the officers during a bunting chantey, where you were too high up to be heard or if heard, identified. And of course "Leave Her Johnny" was a time to air grievances, personal and otherwise. Even so, probably not at the expense of the wife or daughter of someone within earshot and who might still be in a position to apply a belaying pin to one's pate.