Jennifer,
Re old sea chanteys: based on what I know about their history and origins, there weren't many true chanteys before the 18th century. Chanteys -- sailor work songs -- started coming into their own in the mid-1700s and peaked around the time of the Civil War.
This lack of older chanteys may be due in part to the fact that no one collected them. Sailors used them only at work on board ship or at the docks, so they wouldn't have showed up in tune books or broadsides, and it wasn't until the 19th century that anyone became interested in collecting them. One of the oldest, according to Stan Hugill, is "Haul the Bowline" which he dates as an older chantey because the bowline was an important line in early 18th century vessels, but was obsolete technology by 1800.
Don't you just love how there are so many people who carry around such incredibly trivial knowledge?
Have fun, JB