The version in Nigel Gatherer's "Songs and Ballads of Dundee" is very similar to that in Ferrara's post above, but it does have an extra middle verse.
He says it is "as sung by Stewart Brown".

I have capitalised any different words from Ferrara's posting, and there are other minir differences such as ye/you.

THE BALAENA
1.
There's a noble fleet of whalers a-sailing fae Dundee,
Weel manned by British sailors, TO WORK UPON the sea;
On the Western Ocean passage, none with 'em can compare,
But the smartest ship to make the trip is (the) Balaena I declare.

Ch: For the wind is on the quarter and the engine's workin' free,
    there's no another whaler a-sailin' fae Dundee
    Can beat the AULD Balaena, so you needn't try her on,
    For we'll challenge all baith large and smA', fae Dundee tae St. John.

2.
There's the new built Terra Nova, a model with no doubt,
The Arctic and Aurora you've heard so much about,
AN' JackMAN's model mail-boat, the terror of the seas,
Couldn't beat the AULD Balaena on a passage fae Dundee.

3.
Now it happened on a Thursday, four days we'd left Dundee,
An' the wind blew on the quarter-deck just aff the main ye see,
An' carried away oor bulwark, oor stanchions an' oor rails,
An' we left the whole concern, ma boys, a-floatin' in the gales.

4.
BOLD Jackman carries canvas, an' FAIRLY raises steam,
An' Captain Guy in the ARRAN boat goes ploughing through the stream,
And MullEN declares the Eskimo could beat the blooming lot,
But to beat the old Balena, boys, he'd find it rather hot.

5.
And now that we are landed, where the rum is VERY cheap,
We'll drink success to the Captain for ploughin' us o'er the deep,
A health tae a' oor sweethearts, an' tae our wives sae dear,
Not another ship could make the trip but the Balaena I declare.