If you are going the cardboard route, these
ebike boxes are awesome. They are much beefier than regular bike boxes, and wide enough to comfortably fit wheels and other stuff. Not only is the cardboard "finished" on the edges, but the way it is constructed-separate top and bottom opening like a box of chocolates- There are two layers of cardboard all around the outside.
At $40 they are cheap enough to ditch at the arrival point on one end of an open-jaw trip if you need to, and, since before assembly they pack flat in a package only a little bigger than a regular suitcase, it is cheap and easy to have them sent to a departure point.
You do have to warn/encourage/politely ask TSA to open it properly. I've left notes on the box and that has worked.