The song is also known as Queen Mary's Escape from Lochleven Castle (Push off, Push off and row with speed).
Since this old thread first appeared, I found the song and old lyrics on the Levy sheet music site.
I still sing my own lyrics and people tell me they prefer them over the old ones.

Years ago one night at our session, a guy came over to me and asked me to sing my
song (Arran Boat) and while I did, he got on one knee and pulled out an engagement
ring to propose to his girlfriend. It is a beautiful tune.
My lyrics start with "Oh, my true love is sailing his Arran boat, sailing his boat on the silvery sea.
See how it glides as the swans on the even tide, he sails his Arran boat back home to me."

Alice