Stevenson's text is quoted here at

Skye Boat Song  2001-2007. Discussion including Stevenson's words, the tune and some debate on its ancestry, various additional words set to it including parodies.
OVER THE SEA TO SKYE (VARIANT)  DT file.
Syke Boat Confusion  2006 discussion, including details of how Stevenson came to write his set of words specifically to the existing tune.

Any variation in the melody is probably a recent innovation; you may just have to learn it from that YouTube clip if you want to use it.