I have a sort of mid-Atlantic accent and I also love Scottish songs, so I can sympathize. I'd have to agree with Scabby Doug. I like to anglicize words if that works for the song. Keep the dialect if it's necessary for the essence of the song.

On some songs, I've found that singing in Scots interferes with the performance. It's as if the dialect gets between me and the song. It may be that the effort to be "authentic" tenses me up.

If you have really made the song your own, I think you'll know what works.

If you are looking for an example of an American singer who can do Scots songs beautifully, I would recommend Sara Grey.

Edmund