1. "Skin" and "flay" are both commonly used slang synonyms for the verb "whip." Despite the fact that mules don't respond well to whipping, the term "mule-skinner" suggests someone who whips them severely to get them to pull. It may have played on a popular but misguided notion that driving mules requires heavier use of the whip than driving horses. It may even have been used tongue-in-cheek by the mule-skinners themselves, in the same way that carpenters use the term "wood-butcher."

2. "Captain" is also used for John Henry's boss, in a tunnel-blasting crew. It's not specific to mule-driving.