The other short answer for pure marine work is - probably not. The last that I know about was collected by Roger Abrahms in the Carribean in (I believe the mid-60s) with island natives using deep-water shantys to hunt black fish or move houses. Its available from CAMSCO http://www.camsco.com/ as Abrahams, Roger D. Deep The Water, Shallow The Shore- Published 1974, American Folklore Society. This book surveys the importance , historical and contemporary, of sea shanties in the British West Indies. Hardbound Book $45.00. The realy hard thing to find are the field tapes that supported the book. Absolutely magic!
Another loss is that I believe all of our direct connections with shantying under sail (Stan Hugill and Eric Illot among others I'm sure) have "swallowed the anchor.
I tried hard to find shantying in the Arabian (Persian) Gulf in the early 80's and the Gulf of Guinee in the late 60's with no luck.
Anybody know of more recent sources or finds?
Having said that Sail Training Association http://tallships.sailtraining.org/ affiliates, where ever are your best bet to recreate the experience.
Regards, KC