Here's a few corrections and historical notes:

Vs. 1: "Where we watered our shipping.."

Vs. 2: "Now the first we come up with.."

Vs. 5: "But brave Admiral Benbow for help would not cry,
Take me down to the cockpit, there is ease for my smarts.."

Vs. 6: "To see Admiral Benbow carried to.."

The song describes a battle between Benbow's squadron and a French squad that took place from August 19-24, 1702, in the Caribbean. On August 24, Admiral Benbow's leg was severely broken in battle, and I assume he expired from the injury. One of the other ship's captains, Richard Kirkby, was later court-martialled for cowardice and sentenced to be shot, after reports that during the battle he spent most of his time "dodging behind the mizen-mast and falling down upon the deck on the noise of shot...", thus discouraging his men greatly. Printed versions of the song include a verse after verse 5 describing this:

"Our brave Captain Crosbie* proved coward at last,
For he stood at bo-peep behind the main mast;
He stood at bo-peep and did quiver and shake
For fear that those French dogs his dear life should take."

*The broadside this is taken from used the name Crosbie instead of Kirkby. I don't sing this verse myself, but I think it's kinda fun to know the historical background of the song! I got this info from a musty old book "Naval Songs and Ballads" put out by a British Royal Navy Society at the turn of the century. They have a lot of historical info on the songs they printed, and illustrations of some of the ships.