Back in the days when those were made, they glued the paper onto the boxes with animal glue... made from rendering horse and cow hooves and proteins. After decades of sitting shut up, the boxes can smell REALLY BAD as those glues age. There's a name for the glue but I forget what it is.
I just put some OdorEaters charcoal shoe inserts in my box, and it cleared up the stink. I like your idea of stripping down the box completely, and refinishing it. You'll have a nice case that way. Would love to see it when you finish.