Yes and no. You may ship a firearm to yourself, in C/O another person at a location in another state. The recipient should be instructed not to open the package.
Now, the no part of the answer. Since it is a handgun, you can not mail it via USPS. It must go by Fedex or UPS. Getting UPS or Fedex to accept your shipment is the no portion of the answer. If you can get them to take it for shipment, it is perfectly legal for you to ship your handgun to yourself, C/O another person in another state.
http://www.atf.gov/firearms/faq/faq2.htm#b9(B9) May a nonlicensee ship firearms interstate for his or her use in hunting or other lawful activity? [Back] 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.