You might be able to ship eggs via Fed Ex or UPS but live animals ship only via USPS. Express mail will not change, it will still be 1-2 days. If hatching eggs are marked properly, they are handled like live animals and are treated like express mail, even if you don't pay for express. You do have to be careful about the time of year that you ship. The trucks transporting mail are not heated or air conditioned in the cargo areas. The contractors and mail handlers are careful. Chicks and eggs are pulled off the cold/hot docks and handled with care. I'm proud to be a postal contractor and I see first hand what happens behind the scenes.
I have hatching eggs coming from 2 shippers this week. Honestly, I'm a little concerned because it has been so cold here in So OR. The cold is really my only concern.