shortrange,
Any gluing should be done from the inside of the box. Find some thin matching cardboard to use for the repair, and if it is thin enough and you do the entire perimeter of the inside of the box, it will be almost undetectable if properly done. DO NOT PUT THE SEEMS OF THE NEW CARDBOARD OVER THE CORNERS OF THE BOX. Let the seems meet in the middle of the long sides of the box. This way you have strength in the corners which are the weakest part of the box.
If you do not have any this cardboard available, a heavy gauge Kraft paper will do the trick. You can use good old Elmer's white glue and a straight edge to apply the Kraft paper. Get it tight in the corners.
If you have any of the surface color missing from the outside of the box, you can make your repairs and if it is still not to your satisfaction, you can mix up some paint and airbrush the repair (assuming you can get a hold of an airbrush). I usually try to avoid that part because the paint color never quite matches 100% and I wind up painting more of the box than I like to to blend it in.
I once had a box that was so old and so beaten up, I actually made a new box from a sheet of acid free mat board (from a frame shop). I reused the top of the original box for the graphics, and it actually came out pretty good. I used a colored mat board as close to the original color as I could find and I used white rag paper and glue to hold the box corners together. After the box was made (using the original top) I used a bone to work the seems to soften them, as the new edges were too sharp looking.
Eventually I sold the gun with the box, but it was a good experience learning how to do this. I am sure it won't be the last one I have to repair or rebuild as I LOVE old guns, and dislike the new ones!!
Chief38