Hi Spaceboy -
I think the best would be if you could get the instrument playable without doing any major modifications or whatever..
The most likely components that will need to to be changed are electrolytic capacitors - I wouldnt even power the theremin up until these have been inspected / replaced. You could remove the guts from the batteries to retain their shells, protect these with epoxy or whatever, and have space inside to fit available / accessible Lithium cells.
If this instrument has germanium or early silicon transistors, it is possible that dopant in these will have migrated over the 55 years, and these will be dysfunctional or semi-functional, and will need replacing - Personally I would test these transistors before applying power.
But obtaining some information from Moog, if this is available, is a wise first step IMO.
I think that a working instrument is likely to be more valuable than a dead one, even if a few components have been replaced - Clara Rockmore's theremin was brought back to Life by Bob Moog, and I suspect its even more priceless because it works than it would be if it was just a dysfunctional museum piece.
Fred.