You can hear the episode from archive.org here. As I began looking up my favourite episodes of Escape in their original print form, "Snake Doctor" is one I only recently obtained, via the 1923 hardcover Snake Doctor and Other Stories. It's interesting to note that while the radio program gives the hunter a son, there's no such character in the original tale - it certainly suits radio for him to have someone else to speak with and fits seamlessly with the rest of Cobb's tale.
Something I realized while reading Cobb's original text is that the Snake Doctor was a Caucasian man; not that he was portrayed as African-American in the radio version, but somehow it made to sense to me to assume that an unspoken reason for the hunter's intense hatred for Snake Doctor was simple racism; reading the text, however, it's clear that Snake Doctor was supposed to be white. In Cobb's other stories, it's also extremely clear which characters are black (there are instances of the n-word-I'm-too-ashamed-to-type).
I had also hoped Snake Doctor and Other Stories would open me up to more of Cobb's work, considering how much I think of the titular story (it also won the 1922 O. Henry Prize). However, said Other Stories don't possess the tense thrills of "Snake Doctor." They possess some simple humour and charm (plus some unfortunately-expected racism) and a certain longing for one's old Kentucky home, far, far, away. Cobb was an immensely popular US author in his day, but he's virtually forgotten today; we OTR fans who enjoy the Escape adaptation of "Snake Doctor" are probably doing more than anyone else at keeping his name remembered.