I did a quick Google search using "songs sung by pirates". Here are two quick items and I am sure there are more. You will have to wade through other related stuff. You might also PM Masato Sakurai.

http://www.boggandsalty.com/bogg_new/blank2004.html?piratemusicians

... Collected in this book are the music and lyrics of over 60 sea songs, shanties, and ... Presented here are songs pirates would have sung, songs about pirates ... http://www.deadmentellnotales.com/page/DM/PROD/RB/NQGS

In 1928 a young writer named Helen Creighton, was asked to research a story about Nova Scotia's pirates. She had never heard any local pirate stories, so she drove from her home in Dartmouth to the mouth of Halifax Harbour, at Eastern Passage. There she met Enos Hartlan, who not only told her pirate stories, but sang pirate songs. "That," said Helen, "is when the light went on."....http://www.novascotia.com/multimedia/music/songs.htm