It is always presented as being a "Maine Folk song" but in my (informed) opinion, it does not have the "bite" of a Maine vernacular song. My partner Fred reminds me of a fellow from the Wiscasset area named Albert Bailey who was writing songs for his children and friends. His daughter gave me a folder of these songs several years ago and the style certainly seems similar ("comical" songs about clamdiggers and fishermen" Since Boothbay is basically next to Wiscasset, I think it's a good bet that he wrote it. My copy comes from the Bagaduce music library in Blue Hill ME

It also appears here
www.traditionalmusic.co.uk/top-folksongs-chords/boothbay-whale.htm

The Folksong Fake Book

https://www.harptabs.com/song.php?ID=15600

Songs of the Sea, Rivers, Lakes and Canals by Jerry Silverman
https://books.google.com/books?isbn=160974974X

The Boothbay Whale

It was way up north in Boothbay Harbor
Where the water's always cold,
The fisher folk are a clever lot,
Or so I have been told.

Chorus:
Blow hi for his big black head,
Blow low for his big black tail,
Now step right up and take a little swig
And you'll soon see a Boothbay whale.

They catch their pollack, cod and Cusk
By the mouth, the fin or the tail.
One day they got a heck of a jolt,
When into the bay swam a whale.

Says Captain Pete, "I've harpooned tuna,
And caught them with my rig,
But I can't gettin' near no eighty-foot whale,
That fish is too darned big!"

Well, Skipper Jake was a ready man,
Though he had a wooden leg.
Says he, "I think I'll catch that whale;
Let me have that old rum keg."

Well, he stood on the bow of the Nancy U.
And followed that whale for a ride,
And when that whale she surfaced and blowed,
He steered her to starboard side.

The whale blowed steam from his big spout hole
While Jake took a slug from his keg;
And before he could dive, Jake jumped on his back
Hangin' on with his one good leg.

Well, Jake took his keg and used it like a plug,
Pushed it tight in the old whale's spout.
He kicked it hard, then jumped on board,
Saying', "Boys, it will never come out."

Well, the whale he blew, he puffed, he heaved,
And the boys all gave a shout;
And the very next time he rose to blow
He blew his brains right out.

You bold seafarin' whalermen,
You've wasted all these years,
With race boats, harpoons, ropes and hooks,
And all that other gear.

All you need is a big old plug
Next time you see him spout,
Just kick it in, sit back and rest,
While he blows his brains right out.

If you ever meet a fisherman from Boothbay, Maine,
And you want to hear a dreadful tale,
Well, step right up and offer him a keg,
And learn how to catch a Boothbay whale