Well, I finally did track down a recording of this song made back in 1960 as sung by Bill Bonyun on SONGS OF YANKEE WHALING, Heirloom Records. It's very similar to the version in the DT but more oriented to whaling:

JACK WAS EVERY INCH A SAILOR

Now, 'twas twenty-five or thirty years
Since Jack first saw the light;
He came into this world of woe
One dark and stormy night;
He was born on board his father's ship one day
As she was a-lying to,
'Bout twenty-five or thirty miles
Southeast of Santa Cruz.

Chorus:

Jack was every inch a sailor,
Five and twenty years a whaler,
Jack was every inch a sailor,
He was born upon the bright blue sea!

When Jack grew up to be a man,
He left Nantucket Shore,
He went hunting for the whale fish
As his father did before;
One day all in a pea-soup fog,
He met with a heavy gale,
And Jack was swept into the sea
And swallowed by a whale. (CHO)

The whale went straight for old Cape Horn
'Bout ninety knots an hour,
And ev'ry time he'd blow his spray,
He'd send it in a shower;
"Oh, now," says Jack unto himself,
"I must see what he's about."
He caught the whale all by the tail
And turned him inside out. (CHO)

Bill noted that:

"This ballad about a latter-day Jonah apparently originated in a New York music hall and captured the fancy of visiting sailors from all over the world."

Cheerily,
Charley Noble