AZSenior,
As noted, the rules for long guns and hand guns are quite different.
The US Postal Service WILL accept long guns for transport to a licensed FFL. The USPS WILL NOT accept hand guns for shipment!
UPS & FEDEX will accept hand guns for shipment to a licensed FFL - BUT - only via Next Day Air - which is quite expensive - but doable. So...the direct answer is to make contact with an FFL where you plan to be in Alaska to accept receipt of your hand gun and deliver it to you when you arrive. And of course, it will need to be done in reverse when you return from Alaska.
(You may find it about the same cost to :
* - purchase an appropriate used hand gun in Alaska,
* - keep it for the duration and
* - then sell it back before the trip South.)
A quick web search will get you to the actual rules and directions to do the shipment.
2001 National Tradewinds 7370 mid-entry DP w/CAT 3126b Diesel
Look for the Mardi Gras 'Gators - Laissez le bon temps roulez - Let the good times roll!!