Well, the Privacy Act of 1974 (2015 edition) calls that authorized disclosure. In simple terms, the State of Hawaii cannot disclose personal information to the FBI's RAP-BACK system before notifying the owner of the data (you). That affords you the opportunity to decide whether you want to provide that information on the application. While it may result in delay or denial of the application, they can't force you to authorize release to outside parties.
Consent does not have to be explicitly given through a separate signature or initialed box. It can be added to the instructions of the application: "By providing this information, you consent to having your fingerprints entered into the FBI NGI RAP-BACK system for monitoring by HPD." or something similar.
Since that horse already left the barn, they can not go back in time and force you to participate under threat of revoking an existing registration.
§134-3 Registration, mandatory, exceptions
(b) All registration data that would identify the individual registering the firearm by name or address shall be confidential and shall not be disclosed to anyone, except as may be required for processing the registration
or as may be required by a law enforcement agency for the lawful performance of its duties or as may be required by order of a court.
Adding you to the data base could/would be considered lawful performance of its duties
ALso
(b) CONDITIONS OF DISCLOSURE.—No agency
shall disclose any record which is contained in a
system of records by any means of communication
to any person, or to another agency, except
pursuant to a written request by, or with the
prior written consent of, the individual to whom
the record pertains, unless disclosure of the
record would be—
(3) for a routine use as defined in subsection
(a)(7) of this section and described under subsection
(e)(4)(D) of this section;
(7) the term ‘‘routine use’’ means, with respect
to the disclosure of a record, the use of
such record for a purpose which is compatible
with the purpose for which it was collected
also
(7) to another agency or to an instrumentality
of any governmental jurisdiction within or
under the control of the United States for a
civil or criminal law enforcement activity if
the activity is authorized by law, and if the
head of the agency or instrumentality has
made a written request to the agency which
maintains the record specifying the particular
portion desired and the law enforcement activity
for which the record is sought;