I deal with UPS and sometimes they dont know their own regulations. Its best to get on the web sites and copy the regs and have them with you.
UPS- shipping a pistol will be next day shipping , rifles and shotguns can go ground , if you dont have a lisence the rifle or pistol must go to a FFL or Manufacturer . If you have a C@R license ,have it with you and the C@R lisence of the buyer.C@R holders can ship C@R rifles and pistols out of state to other C@R holders or an FFL and receive C@R firearms to their home.
Go to the ATF web site and look for the firearms rules of your state for shipping within state and any rules for pistol registration .
You can also call the nearest state police post and ask them.