's suggestion, I listened to "Speed Gibson of the International Secret Police", a classic juvenile adventure radio serial
that aired from 1937 to 1940. It's entire run was written by Virginia Cooke.
What fun this was! Lot's of "golly, gee whizz" and amazing disguises - but also mind-reading devices and death rays. So if you are OK with categorizing the futuristic technology in "James Bond" or "Mission Impossible" as SF, then this certainly qualifies.
The episodes are very short, and I feel are really are best appreciated together rather than as individual episodes, so I will be nominating them in Best Dramatic Presentation (Long Form) rather than Short Form.
In 1938 the First Adventure ended and the Second began, so I will be nominating "Speed Gibson" in two nomination slots in Best Dramatic Presentation (Long Form):
- Speed Gibson of the International Secret Police - The Case of The World Vs. The Octopus Episodes #45 - #100
- Edit: As "The Atlantian Expedition" continued into 1939, it's not eligible for the 1939 Retro Hugos
Speed Gibson of the International Secret Police - The Atlantian Expedition Episodes #1 - #42
You can listen to the episodes in a number of places online, including here
is an excellent resource for airdate information