I would suggest that anyone shipping a cue should go the hardware store and buy a piece of heavy walled PVC pipe and cut it to size, a 10 foot section will cost you around $7.00 or less and cut in two will ship two cues and you can literally run over it with your car and not damage the contents.
For the ends you can buy plastic caps that slide over but they are a little costly, about as much as the pipe section for each end, what I used to do was cut very heavy cardboard in a circle to fit on the end and just duct tape it in place, works great.
Wrap the butt and shaft section separately in bubble wrap and snug them into the pipe then put the pipe in a box.
I shipped tons of very expensive fishing rods this way up to 9 feet long and never had one broken using this method.