The book is called Aithris is Oideas, published by the Scottish Council for Research. Traditional Gaelic Rhymes and Games, 1964.
I have floated this suggestion over the years but never received any agreement from any of the the Gaelic societies I spoke to. MacGregor's version looks like a small change to existing lyrics. I never believed the chorus was totally nonsense, as stated my MacGregor, and on reading the children's poem is seemed obvious that animal sounds were being represented.