In general, regular Sealed Lead Acid and Gel batteries can be shipped to Hawaii in a properly marked carton.
We do not ship Lithium Ion batteries as they are VERY difficult to ship via air. Most carriers have tight requirements for shipping Li Ion batteries in aircraft. It can take as much as two weeks longer while the carton and battery are studied and it's not unheard of to have the shipment simply returned. Because of these challenges we don't ship them to HI or anywhere that requires air shipment.