Honorable Mentions:
In comments, below, SteveHL draws our attention to a streaming archive of the first episode of NBC Radio's Anthology, a 1954-55 series about poetry, which features a good interview with Sturgeon (and Helen Hayes reading Julia Ward Howe, among other bits and pieces).
The flipside of this Radiola release is the Beyond Tomorrow (CBS Radio, 1950) adaptation of Sturgeon's "Incident at Switchpath"