In my personal opinion (I accept that others may not agree) Some songs require the singer to attempt a version of the original accent/dialect.
"What have you been doing (or where have you been) since the last time we met" does not have the same impact as "Where hast tha bin since I saw thee?"

If you can replicate the sound of the original then 'go for it'.
If you can't replicate the sound, then maybe the song isn't for you.

Of course, there will be people who can't replicate the original sound, but can make the song sound authentic with their own accent. This is known as (part of) the folk process.

I'm happy to sing songs (almost any songs) in my own voice, but some songs will get me imitating (not quite the correct word) the person from whom I first heard the song. So 'McGinty's goat' will always seem to be a take off of Val Doonican. This is because it just doesn't sound quite right if I allow a Welsh accent (and I don't have much of one) to creep through.

Feel free to agree with me, or to tear my comments to pieces!