For the Scenario B ReadyPost you can use any of the ReadyPost mailers... bubble, padded, box, etc. For Scenario A, which they do call "Regular Box Shop", the Guidelines repeatedly refer to using a "box"... not any other kind of packaging.
I've never even thought about using something else, because I have so many perfectly-sized boxes to re-use stacked up in my house anyway!
But since they use the term "box" exclusively and repeatedly for the Scenario A "Regular Box Shop"... just to be safe, I'd use a box.
Practitioner of the Nerdly Arts.