Wilderness Apiary in Port Angeles, Wa uses a 5X7X1 inch single cost box when shipping from 1 to 12 queens, then goes to an slightly larger box as quantities increase.
It is important to give enough air space inside the box, and ventilate it. A few 3/4 or 1" holes with window screen glued over them works wonders. Thos postal boxes can be stiffened with tape on the edges too. It is porbably to most cost effective way to ship queens, your shipping cost doesn't go up whether you ship 2 queens or 10 queens, only when you go to sufficient quantity to warrent a larger box.