Ha! Thanks Charley. I totally missed the sentence where she said she found Stuart Frank's book. Sorry, Mary!

Another approach would be to look at all the primary and secondary sources you can find about Pirates and see whether any songs are mentioned therein. One thing that's neat about Amazon.com: some of the books have a "look inside" feature that lets you look at the index. I just peeked at Pirates by Angus Konstam, and found that there is no index entry for song, singing, or music. Sorry!

But David Cordingly's book Under The Black Flag has a few mentions of "Music at Sea" in its index. Sadly, I have this book, but it is packed away (I move house in a couple of weeks), so I can't look to see if it would help you!