[Phlogiston]

Yes, shellac can turn black, green or white with age and moisture but so can lacquer.

Here is a Wurlitzer that turned white:

   

Your radio could have been finished in shellac or lacquer. It looks like somebody tried to brighten up the yellowed finish. This would be justification (for me) to refinish it. It will be an awesome cabinet if done properly. You can test for shellac in a hidden area by applying alcohol on a rag to see if the old finish will dissolve and lacquer thinner to see if that "top coat" is poly which will get soft, but not wipe off. Hope it is not poly.

Be careful with the solvents.