I've only ever heard 2 people sing "McShane" - Eddie Furey, and also Bill Leiper, living in Aberdeen in the 1970s, who almost certainly got it from Eddie Furey.

With only a few minor changes to above, here's what I'm hearing Eddie Furey singing :

McSHANE

1. My name is McShane from the plains of Kildare
A farmer I was 'til the last year
'Til I took a notion of higher promotion
Went over to England the harvest to share

Chorus: Rum Toora La, Rum Toora Laddie,
Rum Toora La, Mush- a-rum Toora Lay

2. I parted with Molly so blythe and so jolly
Picked up a stick for a staff in me hand
And to keep meself cheery for fear I got weary
I sang "Paddywhack" as I went on me way.

3. I landed at Dumbarton on a fine summer's evening
Me bundle and staff I held them in me hands
There were some of them laughing and some of them chaffin'
More of them trying to stick Paddy away.

4. I went in to a woman to ask her for lodgings
She said "Me young man, now don't look so dull
For I will tell you where you will get lodgings
With a woman that lives next door to "The Black Bull".

5. So I went to this woman and asked her for lodgings
She instantly showed me to a bed in the room
And I being so tired, and worn out from walking,
I threw meself down in me bed in the room.

6. But a lump of a tinker lay up in the corner
He swore 'pon his soul sure he'd kill all was there
Says I "Me bold tinker, give over your braggin'
I'm bold McShane from the plains of Kildare!"

7. But he tried for to hit me a punch in the stomach
I instantly fetched him a one in the throat
And he tumbled heels over his head in the corner
Cut all his head in an old rusty pot.

8. He lay on the floor, like a sheep he was bleedin'
I swore 'pon my soul sure I'd cut off his life
But I lifted him up and sent down for a noggin
Me and the tinker we ended the strife.

9. My name is McShane from the plains of Kildare
A farmer I was until the last year
Till I took a notion of higher promotion
Went over to England the harvest to share.