The conversation seems to have strayed from your original question! Mothballs are bad because their ingredients are poison and can, theoretically, contaminate the honey you harvest. They are also potentially harmful to the bees. But your question was whether or not you can use the boxes again, they having been exposed to mothballs in the past, not whether or not you should use mothballs.
If the boxes are well aired out you might try giving them a good scrub with soap and water then letting them dry in the sun. In my opinion, after that contamination would be pretty minimal.
I don't think it is worth scrapping the equipment. But that is just my personal opinion and not based on science or anything.