I have had good success using a commercial rust remover followed by some elbow grease with wire brush and emery paper then spraying with a cold galvanising spray. It may not look exactly the same as the original finish but it is easy to apply (no primer needed) and it gives a good finish that does not look out of place in a vintage radio.
https://www.screwfix.com/p/no-nonsense-zinc-galvanising-spray-paint-silver-400ml/40801#_=p