Just have it in a Locked Case along with you on your Commercial Airline flight.
Reg'd it with HPD after arrival.
HRS 134-2(f):
"In all cases where receipt of a firearm is had by mail, express, freight, or otherwise from sources without the State, the person to whom the permit has been issued shall make the prescribed entries on the permit, sign the permit in ink, and cause the permit to be delivered or sent by registered mail to the issuing authority within forty-eight hours after taking possession of the firearm."
HRS 134-3(a):
"Every person arriving in the State who brings or by any other manner causes to be brought into the State a firearm of any description, whether usable or unusable, serviceable or unserviceable, modern or antique, shall register the firearm within three days after arrival of the person or of the firearm, whichever arrives later, with the chief of police of the county of the person's place of business or, if there is no place of business, the person's residence or, if there is neither a place of business nor residence, the person's place of sojourn........."
Call HPD and ask about the precise procedure. Most Mainland Military Families bring their Firearms this way to the Islands
18 U.S.C 922(a)(3) and (5), 922(b)(3), 27 CFR 178.29, 178.38
"A person may only buy a firearm within his own State except that he may buy a rifle or shotgun, in person, at a licensee's premises in any State, provided the sale complies with State laws applicable in the State of sale and the State where the purchaser resides."
Notice it says from a "licensee's premises"; you cannot obtain it thru gift or private transfer. Also, it must be legal in BOTH States. Some states do not allow non resident purchases.
Transportation of firearms, "Notwithstanding any other provision of any law or any rule or regulation of a State or any political subdivision thereof, any person who is not otherwise prohibited by this chapter from transporting, shipping, or receiving a firearm shall be entitled to transport a firearm for any lawful purpose from any place where such person may lawfully possess and carry such firearm to any other place where such person may lawfully possess and carry such firearm if, during such transportation the firearm is unloaded, and neither the firearm nor any ammunition being transported is readily accessible or is directly accessible from the passenger compartment of such transporting vehicle: Provided, That in the case of a vehicle without a compartment separate from the driver's compartment the firearm or ammunition shall be contained in a locked container other than the glove compartment or console."
This is a preemptive law -- local and state governments cannot take this right away from you, the Federal law preempts all local and state governments
Also, call and visit the specific Airline you are taking. each Airlines has it own policy not nessecary the same as FAA regulations.