Again, that relates to Scandinavian, not Irish, myth; though there is a chance that the swan in the refrain of that particular version is an Irish touch, swans being a popular motif there. The song was quite widespread in Scotland and England (and later in America) from at least the second half of the 17th century, but has only rarely been found in Ireland; though part of McKennitt's text is from a set noted by Frank Kidson from an Irishman in Liverpool around a century ago. McKennitt appears to have got the song from Roy Palmer's Everyman's Book of British Ballads, where the fragmentary 'Kidson' text is augmented from other sources, chiefly Scottish. Her arrangement follows exactly the same pattern, with the usual trivial changes in words and word-order. It's hard to be 100% sure, though, as she seems rarely to bother to acknowledge her sources. I think she made up her own tune.