I would be surprised if it isn’t lacquer most old radios are, with the exception of some really old ones that were shellac. (french polished)
Depending on your skill level you may want to consider wheather it is necessary to refnish and how to do that. some radios need to be stripped, some don’t and sometimes you are better off just hiding the scratches with a finish such as wax or even an oil finish, just where the scratches are. It is sometimes possible to use an amalgamator to blend the old finish into a new finish which is sprayed overtop, but I have seen varied results with this technique. what you don’t want to do is to trap dirt between the layers. of course if you strip you’ll likely need to make some new labels so if you go that route I would try to at least get good photos of the labels you have , for tone , volume etc.