I can't say what it would cost, but most places that do high end custom boxes have a high minimum. The places I checked into had a 1000 piece minimum on each size. I've looked everywhere, and have had no luck finding a company that will do small quantities. You may have better luck with custom printing on a stock box. Nashville Wraps has a better selection, and they do custom printing and labels.
I have custom boxes. 6 piece cost about .90, 12 piece about the same. The 24 piece was 1.70. I think I ordered 2000 6 piece, and 1000 of the other two. Most places will do small runs, but the price is prohibitive.
I like to change up my packaging for seasonal runs, and could not afford money or space wise to have so many different boxes printed up in large enough quantities to be cost effective. I went to ebay purchased a second hand (actually two of them) hot foil printers. I now run what ever boxes, bags, gift cards, and my own ribbon all to match in whatever size run I like. It has become quite profitable, since I can now do custom runs for special clubs, private business's ect. I can run about 50 yards of ribbon and 50 boxes in less than an hour, this includes setting the type. These machines are old (early 1960's,) I have had no problems with either one and paid complete less than 100 bucks. Hot foil is cheap and easily available at most print shops in every color under the rainbow. I also use some high end leather covered boxes and some wooden jewellery boxes for my chocolates as well and this hot foil device works just as well on these items.