Ah....the worrisome (little wanna be liberal)PC's.

Nothing racist to it.....it is a cuckold song.

cotton-eyed adj. So.
1905 DN III 75: Cotton-eyed...Having the whites of the eyes prominent. 1952 Steinbeck East of Eden 228: The crooked little cotton-eyed piano player stood in the entrance.

Lighter, J.E.,Random House Dictionary of Historical American Slang. Volume 1, p 490, 1994.

DN indicates Dialect Notes