In Asia it is more common to ship cardboard boxes and the like by plane, much without issue. Chinese airports have baling machines to even wrap boxes. In your case I would suggest a large enough, transparent plastic "really useful box", which you can cable tie in some holes to lock it closed. It's a firm box that can be used on the other side, and waterproof (cardboard is not waterproof and a little wetness greatly reduces the strength of the box). Also, it's easier to carry with handles compared to a cardboard box.

It's actually quite a neat way to transport things when you don't want another suitcase and you have a large luggage allowance, especially weight concept....