So far as Loreena McKennitt's set goes, she unhelpfully describes her text simply as "traditional", but I'm assuming that it's an American variant; as she uses a tune of her own, it's hard to tell.  A quick search through Google.com brings up a transcription of the lyric, though it's unclear whether it's transcribed by ear or taken from sleevenotes.  This gives the problematic line as "a hey ho bonny o", though the soundclip I found sounds more like "Hey he ho me bonny o"; either is likely, and turns up much the same in older Scottish sets as well.

The difficulty lies in Ms. McKennitt's strange habit of giving a gutteral sound to initial "h" and to some initial vowels, which she may have picked up from Martin Carthy records; he used to do the same when he was in his over-ornamented phase back in the '70s.  She is actually singing "O", though it doesn't sound much like it!

The inconsistency between farmer's and king's daughter isn't all that unusual in traditional sets.  Ms. McKennitt herself had this to say: [It is] "a reflection of the Celt's flight of fancy where it doesn't make a lot of sense" and adds "it's the way the Celts didn't really make a distinction between this world and the next and their own flight of imagination took reign."  (Quote from  Loreena McKennitt Old Ways Mailing List FAQ).

In fact, the flight of fancy is hers rather than any putative "Celt"'s; if she researched her material she'd have known that it's a song of Norse origin which moved from the Anglophone part of Scotland into England and on to America, hardly touching Ireland -though it has just occasionally been found there- and that the Farmer seems originally to have crept in in English versions.  I think it was Bronson who suggested that the Swan refrain was a likely "Celtic" input, but not much else of the song shows great differences from Norwegian equivalents.  Obviously I'm speaking of the text, here; the various melodies used I'm not in a position to enlarge on just now.

Malcolm