In my copy of TYBTM it states

.....His seafaring experiences also led him to prepare and publish (in 1841) 'The Seaman's Friend' (or, as it was called in England, 'The Seaman's Manual'), containing a glossary of sea-terms, laws respecting duties of masters and marines, &c.

In addition to these, Dana wrote several other works, including 'Biographical Sketches', 'To Cuba and Back', 'A Vacation Voyage', besides a large number of reviews, many of which were afterwards collected and published in a volume.

Unfortunately, no mention of sea songs. I have never seen any of his other works, so don't know what they contain.

The Intro goes on to say he died in Rome in 1882. So, if any papers are still in existence, they may not be in the US, anyway.

Brian