I've only packaged fertile eggs for hatching once, but it must have been okay because the person I gave them to had an excellent hatch from them.
I didn't wash the eggs, of course. It took me I think three days to collect the 18 I wanted, choosing only the largest most well-shaped eggs. As I collected them I put them in a paper carton on a counter in a cool area away from the heat vents. Put them in the carton small end down. I put a roll of duct tape (someone told me that this would be the perfect size) under one end of the carton to set it at an angle. A couple times a day I would switch the roll to the other end of the carton. Rotating the ends like this keeps the yolk from settling at one end.
Though I was hand-delivering them, not mailing, I still wrapped the whole carton in some bubble wrap I had handy to avoid any accidents in the car. I'm notoriously clumsey.
Hope this helps.