I think you could count "Haul on the Bowline" as a pre-19th century chantey. Hugill calls it "possibly the most ancient of the shanties." His reasoning is that the bowline was a line of great importance during the Middle Ages, but became less central once fore and aft sails were developed. Plus it's just a great song!

I think if you're doing naval living history, that chanteys weren't really used too much in the Navy. Probably just a "sing out" or a "cry" was all they used.

Where do you guys play? I'd like to hear you sometime.