I had heard that Amazon was selling mp3s of out of print albums, so I took a look to see if they had any shanties. What I found inspired this rather blatantly commercial post:
Boy. Have they got shanties! They have shanties in English, German, and even "Ali alo" in French. You can hear a sample of the song before purchasing (click the little white "play" arrow in the gray box to the left of the song), and some albums have a "Preview all" link at the top of the list of songs. You can buy an mp3 album, or buy just one song (most songs are around $.99). Searching by genre is very general; the albums I saw were listed as "Traditional Folk" or even, "Folk > General." So searching by a known artist or possible title keywords might be a better bet.
And the best news of all: the mp3s are DRM free. From the Amazon music download FAQ:
Digital Rights Management or "DRM" commonly refers to software that is designed to control or limit how a file can be played, copied, downloaded, shared, or accessed. DRM-free means that the MP3 files you purchase from Amazon.com do not contain any software that will restrict your use of the file.
As a hint of how cool I think this is, I have to tell you that I'm an ardent supporter of local, independent music stores (for me, that means Down Home Music and Amoeba Music), so it takes a lot for me to give some free advertising to Amazon--it takes my being thrilled to be able to buy DRM-free out of print music. DRM-free because it tends to work better on my devices, including my mp3 player (a Sandisk, because it can record radio shows while I'm in meetings!). And you can shop Amazon somewhat mindfully--there are many nonprofits which have a link to Amazon that gives them a portion of the purchase price (from Amazon's cut--not yours).