What ground-based, airline job in the 1940s could have involved radio communications?
Perhaps she was a flight dispatcher?

A flight dispatcher (also known as an aircraft dispatcher, airline
dispatcher, flight follower or flight operations officer) assists in
planning flight paths, taking into account aircraft performance and
loading, enroute winds, thunderstorm and turbulence forecasts,
airspace restrictions, and airport conditions. Dispatchers also
provide a flight following service and advise pilots if conditions
change. They usually work in the operations center of the airline.

-Wikipedia