Hi Andy,  Do not refinish that case, it will not be worth what it is now.

I know it will look clean and shiny, but you also lose the original
decals put on by Edison's factory.  But try to sell it and listen to the
comments.  I have been restoring gramophones and music boxes for over
twenty years; I've seen it all the time.

Now what to do.  Well, get a can of "BLACK WAX"; you can get it at
Meritt's Antiques ,1860 Weavertown Rd., PA Box 277, Douglassville, PA
19518-0277 U.S.A.  Phone 1-800-345-4101

It is $ 9.50 for a can that will do you and your neighbourhood .  This is
also what I use on the paint on the bed-plates, too.  Now you can go over
the decals with this, too, but do not rub too hard.  Rub until you hear
the finish squeak, then just buff it with a soft cloth.  Try the nine
dollars before you destroy a finish that gives the Edison its appeal to
us all of the olden days.  Let me know how it goes.

Bye for now

Keith Merchant
B.C. Canada