you can ship in a Pampers box through the USPS but I wouldnt recommend this type of box for anything fragile unless it is very small and you use a lot of packaging.
I see a lot of flimsy packages with "fragile" or something similar on them, and while everyone does their best to handle with care, most customers forget that a large percentage of packages (sent through any service) are sorted by automated equipment and may end up underneath other packages.
If you do use the Pampers box, clearly PRINT the return and ship to addresses on a plain piece of paper and tape to the box with packing tape. Some slick surfaces will not hold marker writing well if the package is being handled by hand.
FYI, anytime you ship anything through any service, its a good idea to put a second address label inside the box. If your label or writing is damaged or becomes illegible, designated employees will open the box to see if anything can identify the shipper/addressee.
ncneighbor