Oh, gee, I should have had a looksee at the Traditional Ballad Index - click here for their information on "High Barbaree" - the earliest known version of the song is 1670.
Click here for their reference on "Henry Martyn," date unknown. It's Child Ballad 250, so it had to come out before Child published his book in the last half of the 19th century. You can Click here for the 1864 sheet music for "Finigan's Wake," and Click here for the Ballad Index information on the song.
-Joe Offer-