I've always felt that the singer should sing the song as he feels it. If that means with an accent, so be it. Most Irish and Scots songs naturally lend themselves to a certain lilt, if nothing else, particularly when they are written in a dialect or they include Gaelic words and phrases. Those songs would sound a bit strange without a least the tiniest hint of an accent. And think of all the white Brits and Americans who've tried to sound like Blind Lemon Jefferson, because they're singing rock or blues. I was amazed for instance, when I found out that Eric Clapton isn't an African American. So, I say, go with the way it feels right, but try not to exaggerate or insult anyone in the process.
When my mother was doing a play by John Synge, called DEIRDRE OF THE SORROWS, everyone in the cast tried to put on an Irish brogue. The director, who was from Dublin's Abbey Theatre, kept telling them that all they had to do was read the lines as Synge had written them and they'd have the right lilt, without sounding like a Cork music hall performer (her words, not mine).