You can export fish out of Hawaii no issues. Importing is another story. It requires special permits.
http://hawaii.gov/hdoa/admin-rules/subtitle-3-division-of-animal-industry/AR-20.pdf
Entry into State. No non-domestic animals shall be allowed entry into the State unless all pre-entry requirements have been met. Landing or removal of non-domestic animals from a carrier for purposes of inspection or quarantine shall not constitute entry into the State for any purpose whatsoever. No effects of non-domestic animals, likewise, shall be brought into the State unless so authorized by an inspector of the department.
Ports of entry. (a) Non-domestic animals subject to testing requirements shall be entered through Hilo or Honolulu, where livestock testing and quarantine facilities are provided. (b) Non-domestic animals subject to rabies quarantine shall be entered through Honolulu, where the State's only rabies quarantine station is located; however, animals of this category may, on approval of the board, be quarantined under supervision of the division at an official state, county, or municipal zoo. (c) Non-domestic animals subject to inspection only may be entered through any port or airport in the State.
Carrier responsibility. (a) Carriers transporting non-domestic animals through any port in the State or landing these animals at any port within the State shall, on arrival, submit a shipmaster's declaration to the department providing the following information:
(1) Name and address of owner, importer, consignor, consignee, and port of origin of the animals;
(2) Number of non-domestic animals on board; and
(3) Number of non-domestic animals which have died en route, with the circumstances of the deaths.
(b) Carriers shall be responsible for securely confining animals for entry at the pier or airport until movement is authorized by an inspector.
(c) Animals in transit to port beyond Hawaii shall not be off-loaded for any purpose unless authorized by the state veterinarian or an agent.
(d) Carriers shall not off-load and dispose of manure except under the supervision of an inspector.
Preshipment requirements. (a) A permit issued by the board shall be required for importing non-domestic animals. Application for the permit shall be made in writing to the chief
plant inspector in advance of importation and shall be subject to conditions imposed by the division of animal industry to prevent the introduction of transmissible diseases. (b) Non-domestic animals for entry shall be accompanied by an interstate health certificate issued by an accredited veterinarian, or a state or federal veterinary officer in the state of origin, within seven days before shipment. The certificate shall give a description and identification of each animal and shall certify that:
(1) The animals described are free from external parasites and symptoms of transmissible diseases and that they have not had recent exposure to these diseases; and
(2) That all preshipment requirements prescribed have been complied with.
Post-shipment requirements. (a) Non-domestic animals for entry shall be subject to inspection by the state veterinarian or any agent. Any indication of transmissible disease or failure to comply with all preshipment requirements shall be sufficient reason to refuse entry or quarantine the animals at premises approved by the state veterinarian. (b) Non-domestic animals subject to any special follow-up testing requirements imposes shall be held under premises quarantine until completion and clearance from such testing.
(c) All expenses in connection with the segregation and treatment or destruction and disposal of the quarantined animals shall be borne by the owner, importer, or consignee.