Not to be the party pooper on the wood box, but I'm starting to wonder about your intent.
Do you mean to build a box to contain the set - i.e., the cardboard box and its pieces inside it - almost like a prop or support piece in a museum, that also serves to preserve and protect the original box, which is flimsy and prone to deterioration or damage in handling? Because that would be cool, I think. Maybe a see-through lid, though, is what I was thinking. Because, well, the graphics etc on the carboard box is all the zazz. And if you had to open a wooden box just to see it, it kind of defeats the point, no?
Or do you mean you are going to replace the cardboard box, put it aside, and put the pieces in a wooden box?