This was one of the subjects at one of Bob Askew's ballad chats at C# House. This bit from the notes that Bob circulated seems worth quoting here.

"It seems to be based on a true event. Joyce said that it was very popular in mid and southern Ireland in the 19th century. He noted the earliest version in Ireland and felt that it was based on a true event: 'it obviously commemorates a tragedy in real life'. An article in Ulster Folklife 1845 quoted a manuscript from Kilwarlin, Co Down, which named James Reynolds and Molly Bann Lavery, born in Lisburn, and educated in Lurgan. The surnames were local, the Laverys were Catholics and the Reynolds Protestants. No archival evidence has yet been found to prove this, but it is likely that it could turn up."

Anyway I think we can discount the theory that the story derives from an ancient belief in swan maidens. The point was made at the ballad chat that accidental shootings are common enough. (Not however to quite the extent satirised by Tom Lehrer.)

I don't understand the mutation rules in Gaelic, but I do know that when "b" changes to "bh" it is sometimes pronounced like "v" (hence Polly Vaughn/Vaughan) but it can also become like "w", which seems a likely explanation for the "Whan" spelling in one of the broadsides.