I've gleaned this information from several web sites:

Ernest Hogan and Chris Smith wrote 'TAIN'T NO DISGRACE TO RUN WHEN YOU ARE SCARED in 1903.

Bob Roberts recorded 'TAIN'T NO DISGRACE TO RUN WHEN YOU ARE SKEERED in 1904.

Bert Williams recorded 'TAIN'T NO DISGRACE TO RUN WHEN YOU'RE SKEERED in 1921 but the recording was apparently never released.

I was unable to find any current recordings or lyrics.