The super-sweet Catholic Gaelic hymnal is Fr. Allan MacDonald’s classic collection from 1893. But unfortunately, there’s no music in it because the islanders all knew the tunes.
Here’s The Sacred Songs of the Gael, an old book of hymns in Gaelic (the Scottish kind). They’re Presbyterian or Church of Scotland or something like that. Anyway, the thing of interest is that the book provides the tunes, with harmony. I don’t know if that’s the real harmony or something made up by the book publisher, but at any rate it’s the real tunes. Lots for folks to steal. :)
A lot of Irish Christmas albums nab some Scottish carols:
“Taladh Chriosta” aka “The Christ-Child’s Lullaby” is from the Hebrides. It was written by Fr. Ronald Rankin, before he went off to Australia in 1855. It’s something like 27 verses long.
“Leanabh an Aigh” (Child of Wonder) has a tune better known in connection with “Morning Is Broken”. Also has about five zillion verses.
Lots more Scottish Gaelic Christmas songs on this page.
“Ny Kirree Fo Naghtey” (The Sheep Beneath the Snow) is a good tune from the Isle of Man, but it’s not actually a Christmas carol. Here are the original lyrics and a translation. It’s actually the horrendous story of how almost all a man’s flocks were killed by snow and cold. (Wow, I wish I hadn’t found that out.)