I always thought all the shipping companies and the post office wants a corrugated cardboard box or something sturdier than a cardboard box. Plus they don't want a bunch of writing or lettering on the box, they want the shipping label and thats it.
Plenty of Postwar accessories came packed in corrugated cardboard boxes.
I have had similar things happen, but it's always been on small items. I try to remember to explain to the seller that I am buying the item because of the box. I suggest you try the hair dryer, as has already been recommended. It often works.