The Arran Boat Song gets its title from a 19th century parlour song "Put off, put off and row with speed" about the escape of Mary Queen of Scots from Loch Leven Castle. The boat was provided by the Earl of Angus and Arran, hence it was called the Arran Boat. Loch Leven is the other side of Scotland from the island of Arran. The tune was chosen by the songwriter to be "The Banks of the Devon" which was very popular at the time and never had anything to do with boats.

The present day instrumental "Arran Boat Song" is simplified a bit from the vocal form. It's in Kerr's Merry Melodies from about 1880. I played it (on an ocarina, I think) in a pub session a few hours ago.