I work for a shipping company as a package handler. I know what kind of tossing around those boxes can get. I'd use one of the insulated boxes packed with newspaper (or packing material of your choice) with a bag in the middle in order to reduce trauma from being bounced around.
You use and empty deli cup and you might as well shake the poor ball to death.
BTW - writing FRAGILE and AVOID EXTREME TEMPS can sometimes help, but NEVER rely on that. most trucks aren't insulated in any way (below freezing in winter and 120 in summer). and a lot of minimum wage workers don't care if they act like Jim Carey in 'Ace Ventura' with your precious cargo.

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