The earliest text yet discovered:

From "The Siege of Gibralter. To which is added, II. Sailor Jack III. The Newry Rangers IV. The Flowers of Edinburgh. V. Bryan O'Lynn. VI. Molly's Courtship to the Jolly Sailor [Edinburgh? Ca1785?], pp. 7-8   


                                   BRYAN O’LYNN.

When Bryan O’Lynn would a wooing ride,
He’d a good Scotch woola [sic] hung by his side;
Its sheath it was made of a good Elk’s skin,
I’m a huffring [sic] young fellow, says Bryan O’Lynn.

When Bryan he went to the church to be married,
And when he came there he was forced to tarry;
The church door was shut and he could not get in,
He’s a fool of a parson, says Bryan O’Lynn.

When Bryan was married and into bed tumbled,
The neighbours they all came flocking in;
He lift up his thigh, and swore by the by,
That he was the famous young Bryan O’Lynn.

The priest that married us he was to blame,
By faith he had neither grace nor shame;
With a ring made of straw contrary to law,
It was with that he married poor Bryan O’Lynn.

Bryan’s wife and his wife’s mother,
They both went over the bridge together;
The bridge it broke and they both fell in,
The devil go with them, says Bryan O’Lynn.


Except for the bridge business (see Tom Bolynn thread), not much like any other version,

Do "woola" and "huffring" mean anything to anybody?