Good heavens, I cannot believe some of the "explanations" given here as to the "meaning" of Shule a rack shack etc.,
There is no meaning, because the words were originally in the Irish language. I've known this song as an Irish song, since well before the 60s when P.P & M. recorded it. Obviously they heard some Irish source and liked the song so much that they wanted to record it. There were plenty of Irish singers plying there trade in the Bars and clubs of New York at the time and some would have known this song. (It does allow that P.P. & M. style)They didn't have time, or maybe couldn't be bothered, learning the Irish words phonetically so, either they or some other agent, replaced the Irish words with some syllables that could be easily remembered and were in the correct meter.
That's all, no Yiddish,no Scottish, no nuttin' else, just plain old Irish. It's a lovely song and P.P. & M. did a beautiful version.