I know it's a year on so I may be too late, but please don't have this stamp box silvered. There appears to be no trace of old silvering, suggesting that the box was always meant to be seen as brass, so you'd kill the value and make a very stylish late Victorian / early Edwardian brass stamp box look garish.
As for the two compartments, the early stamp wetters were made of glass and were seperate from holders. This piece was most likely made to hold 1st and 2nd class stamps, either 'penny blacks' and 'penny reds' or Edwardian 1/2d and 1d stamps.