I think we must define "dialect" as oposed to "accent" here. I don't see anything wrong in a British singer singing a Scotish, Irish or American song and using words from the country of the writer. In your song "Handfull of Songs" Jerry, I would not think of changing the line "His old railroad watch" to "His old railway watch" but because I am not American I would never try to use an American accent to sing this song. I have seen too often English singers singing "Geordie " (Newcastle on Tyne area of Northern England) songs and trying to use a false Geordie accent, and to a Geordie it sounds is sounds auful. Sing the songs by all means but do it your way and don't try to copy an unfamliiar accent.
Bill