What you described, no, I don't believe so.
YOU can ship them to yourself.
YOU can send them to
YOURSELF, in care of your buddy Bob, in your new town, telling Buddy Bob that he cannot open the boxes. That's legal.
But your buddy Frank, here in your old town, cannot ship them to you.
YOU can ship them to you, but as I read the law, someone else cannot ship them to you.
ATF Online - Firearms - Frequently Asked Questions - Unlicensed Persons
#9 >May a nonlicensee ship firearms interstate for his or her use in hunting or other lawful activity? Yes. A person may ship a firearm to himself or herself in care of another person in the State where he or she intends to hunt or engage in any other lawful activity. The package should be addressed to the owner. Persons other than the owner should not open the package and take possession of the firearm.<
Problem is, while you can mail, through the post office, your rifles and shotguns, your pistols have to go common carrier. And UPS/FedEX have a bad habit of requiring an FFL on the receiving end. Even though the law says you can ship them to yourself, quite often FedEx/UPS won't let you.