Although I can't answer your question, I bet a phone call or visit to your local post office and a talk with the post master/mistress could be helpful. (Providing you don't have a frantically busy post office like some of them are. )
It seems like the U.S.P.S would be one of the best sources for how to ship a live bird through the mail, or if you choose another carrier, like UPS then they should be able to give you answers.
Thinking back to the day when I had an antique piece of glass arrive is shards... postal travel can be brutal.
good luck.
Perhaps you will have a chance to post back when you get your answer if no experienced BYCers provide the definitive method.
I guess you could also phone a hatchery or internet source that sells live grown birds, incase they would be kind enough to give you tips.