The American folklorist Roger Abrahams has written something on Caribbean sea shanties. I'm damned if I can remember what it was called or where it was published. But a bit of googling should get results.

Also check Rounder's Deep River of Song. Bahamas 1935: Chanteys and Anthems from Andros and Cat Island. Rounder 11661-1822-2, which has quite a few shanties.

Also, Nonesuch LP H-72013; The Real Bahamas in Music and Song, for a shanty called Sailboat Malarkey by Frederick McQueen.

I suspect that once you start looking, loads of stuff will turn up, both as shanties proper, and as shanties which have been adapted for other purposes. EG Caribbean Voyage: Brown Girl in the Ring. Game and Pass Play Songs Sung by Children and Adults from Trinidad, Tobago, Dominica, St Lucia, Anguilla, Nevis and Carriacou, Rounder CD 1716, has a game song called Coming Down With a Bunch of Roses, which is clearly related to Blood Red Roses.