Interpolating and extrapolating from one citation to the next based song title alone isn't good practice. And I'm not aware of any c.1810 chanty sheet music just yet. It's mostly penny dreadful, nickle weeklies and dime novels. You're lucky if you get two full verses of lyrics.

That said, Théodore Latour and the Prince Regent (George IV) means his sheet music belongs to the Jane Austin crowd: Regency dance. If you know an old-timey dance reenactor they may some of your answers.

And just to dig the rabbit hole a little deeper, in his spare time, Latour seems to have had a go at: O du lieber Augustin (Lieber Augustine)

But wait! That's not all! King George IV was Colonel-in-Chief of the Life Guard (1815–1830) along about the time they took a shine to Faithless Sally Brown (There's na luck about the House) .

Ain't we got fun... and filkies too!