Clean/Restore old cigar boxes from early 1900s

These cigar boxes are from the early 1900s and have some great artwork/stickers on the inside lids of the boxes. While the interiors are in great condition, the outside of the boxes show some damage from dirt/water. 
I want to clean and restore the boxes so I can set them out for display but am not sure how to go about this...

So far, I've dried them out by storing them in a ziploc bag with rice to absorb any excess moisture, and have dusted them off with dry swiffer cloths, foam paint brushes, and compressed air but am not sure how to get rid of the remaining dirt & water stains. 
 
I've searched online and have seen some suggestions to use vinegar or soap & water but I'm hesitant to use liquid as I'm afraid it will cause more harm than good.

Any tips or suggestions would be much appreciated.
Pictures here <
Thanks

I recently came across about 10 old cigar boxes sitting on a shelf in my in-laws barn.These cigar boxes are from the early 1900s and have some great artwork/stickers on the inside lids of the boxes. While the interiors are in great condition, the outside of the boxes show some damage from dirt/water.I want to clean and restore the boxes so I can set them out for display but am not sure how to go about this...So far, I've dried them out by storing them in a ziploc bag with rice to absorb any excess moisture, and have dusted them off with dry swiffer cloths, foam paint brushes, and compressed air but am not sure how to get rid of the remaining dirt & water stains.I've searched online and have seen some suggestions to use vinegar or soap & water but I'm hesitant to use liquid as I'm afraid it will cause more harm than good.Any tips or suggestions would be much appreciated.Pictures here < http://imgur.com/a/moDei&gt Thanks