I'm not exactly sure what constitutes a sea shanty but The Dubliners have various songs about life on the high seas. Try these :
Home Boys Home,
Donegal Danny,
Farewell to Carlingford,
Go to Sea No More,
Irish Rover,
Net Hauling Song, and a really good one is
The Craic Was Ninety in the Isle of Man.
That should keep you going and let me know if they are actually shanties at all.