Here's the version from Joanna Colcord, Songs of American Sailormen , (1938) pp. 194-195.
Colcord's notes:

Captain Bunker of the next song must have been one of that family which sent forth a long line of noted sperm-whalers. The singer identified the song with a Captain Bunker who had died shortly before in Sailors' Snug Harbor; but this is probably an error, as the song goes back to the early days of offshore whaling.

THE COAST OF PERU

Come all ye young tars who are cruising for sperm,
Come all ye jolly seamen who have rounded Cape Horn,
For our captain has told us, and we hope he says true,
That there's plenty of sperm whales on the coast of Peru!

'Twas early one morning just as the sun rose
That a man from the mast-head sung out "There she blows!"
"Where away?" cried our captain, "and how does he lay?"
"Two points on our lee, sir; scarce three miles away."

"Then call up all hands and be of good cheer;
Get your lines in your boats and your tackle-falls clear.
Hoist and swing fore and aft; stand by, each boat's crew,
Lower away, lower away, as the main—yard swings to."

Our waist—boat got down, and of course she got the start.
"Lay me on, Captain Bunker, I'm hell for a long dart!"
Now bend to your oars and make the boat fly,
But one thing we dread of, keep clear of his eye!

Now the captain is fast and the whale has gone down,
And the first mate lies waiting his line to bend on.
Now the whale has come up, like a log he did lay;
Whatever he done, boys, he gave us fair play.

(Line missing)
But we fought him 'longside and a lance we thrust in,
Which caused the whale to vomit and the blood for to spout;
In less than ten minutes he rolled both fins out.

---

Click to play

To me, this sounds like the tune Lou Killen used on Steady As She Goes: Songs and Chanties from the Days of Commercial Sail.