The earliest inkling we have of an actual song describing a female pickup as a boat of some kind is a mere title. Samuel Rowlands's satirical pamphlet "A Whole Crew of Kind Gossips" (1609) gives a list of "baudy songs" known to a real or imagined friend of his, who Rowland claims learned them from prostitutes. Among these is a song called "The Pinnace rigd with silken saile."
A "pinnace" was a boat used to carry messages, supplies, etc., from ship to ship or ship to shore. It became a slang term for a prostitute, possibly because a pinnace sailed around the harbor all day and was available for public hire.
Regrettably no copy of "The Pinnace" survives. (A text circulated in the mid-nineteenth century by the Shakespearean critic John Payne Collier has proved to be Collier's forgery.)
Several surviving songs related to the "Yarmouth" theme appeared during the seventeenth century, though none is really the "same song."