I can't help you with the sheet music.
But one of my favorite sea-shanty performers is a guy named Jerry Bryant. He has a great compilation of traditional sea-shanties that are intended as an accompaniment to Patrick O'Brian's Aubrey-Maturin series (e.g. Master and Commander, etc). It's called "Roast Beef of Old England
Though not traditional per se, he also has an outstanding compilation of original sea-ballads, called "The Ballad of Harbo and Samuelson
Both of these are truly outstanding examples of sea-shanties and sea-ballads. I'd recommend them to anyone for listening or performing.