Having discussed this aspect and thought about it a little (but not enough, yet), I think there are probably some songs where it's acceptable or even desirable to do some kind of imitation of the accent, or they just wouldn't sound right.

There are probably others that it's better not to do this, and just sing in your own natural voice.

But I haven't been able to come up with any general rules about this.

As for Cotton Fields, I wouldn't attempt to sing it in an imitation 'black' voice, not just for PC reasons, but because I don't feel I could imitate that type of accent very well.

But for this particular song, I don't see why you can't sing it in your normal voice (assuming you are 'white') - it's a good singalong song, whatever its origins were. I think this is OK even if you sing "them old cottonfields" instead of "those old cottonfields", which would sound plain daft, IMO. Pity there aren't more verses to it though.

There are some songs I wouldn't attempt - either because I don't think I could do them justice, or because the subject matter doesn't suit my style, mainly.