May I respectfully suggest that you and others who may be interested in my comments and others' comments on the subject of "Pick A Bale of Cotton" visit that thread and read {& possibly join in that discussion {though the specific thread name escapes me and I'm supposed to be doing work so I can't look it up now].
However, I'll summarize my comments to say that-in my opinion- whoever sings "Pick A Bale Of Cotton" whether they be Black, White, or Green should be aware of the fact that many Black Americans believe that that uptempo song minimizes the degradation and horror of chattel slavery which has come to be symbolized by picking cotton. I believe this to be the case regardless of the fact that non-Black folks picked cotton, and regardless of that song's origin, and regardless of whether Leadbelly, and other Black artists sang or sing it.
With regard to the song "Black Betty" I believe you are misremembering my comments. I don't recall indicating that I have any concerns about that song. To the contrary- I like that song. I remember listing "Black Betty" in a thread that I started about skin color references. And I also remember reading [and probably joining in] what I considered to be an interesting discussion about the meaning of "Black Betty". For instance some posters considered "Black Betty" to be a coded referent for a whip. I always thought it was a referent for a woman of dark skin.