I'm not much of a singer, but I think you have to make the song yours before you can really sing it. That can mean anything from working out how it fits your voice, breathing etc. right through to changing whole verses where you disagree with the original, or feel it can be expressed better for you. There might be some difference if the audience is expecting you to give them a comfortably familiar version of a well known song, but I'll sing the Wild Rover, no never, no more.

Or to make the language accessible to the hearers - for example, if I were singing to an American audience, I wouldn't load a song with Lancashire dialect that could be avoided, for example change "Hoo sez as hoo knows when hoo's hurt" to "she says that she knows when she hurts".