As to the origin of the word 'shanty':
Margarita brings up a good point. There is a very strong influence from the various 'slave ports' that ships would do business at. A fair amount of evidence points to some owners selling their slaves to ship's captains as deck seamen so that the owners wouldn't need to support their 'charges' during the off season. The slaves definitely influenced shanties on board, as they brought the plantation and other songs of their past with them.
One of the things that fascinates me about shanties is the incredible diversity in music sources that can be traced. Since the captains were in the habit of picking up crews anywhere they could, the result is a body of tradition where musical influences can be seen from almost every nation in the world.
*Steps down off of soapbox*
The original point of this (yes there was one) was to point out that the word 'shanty' probably owes less to the slave culture than to other regions that the sailors hailed from. I may be off on the timeframe, but I believe that the word 'shanty' was being used at some point in the 1820-1830 range, and from regions that wouldn't have had as much contact from the slave labor. But as has been said, linguists and etymologists have been debating the origin of the word for as long as it's been a recognized word... I doubt that I'm going to solve anything.