First ensure that all the power has been disconnected/removed from the radio before you start.
Use a soft brush (shaving brush is good) to gently loosen any dirt and grime that then can be vacuumed up.
After that use Isopropyl Alcohol 90%+ (available at most pharmacies) and a soft toothbrush to remove any remaining grime etc. If you can avoid it, do not use “rubbing alcohol” as this is usually only 70-80% IPA or less and can contain scents and other ingredients and therefore is not as effective. It can also possibly leave residues. Check the label on the bottle if you have to use it.
The alcohol evaporates and leaves no residue so there should be no electrical problems afterwards.
As always with electronics (and especially with old electronics) be gentle when handling. Do not brush too vigorously and move components about too much when cleaning as you may '“break” their leads or solder connections to the pcb.
Good luck with the cleanup.