You don't really have to "demand" it. You just make it the ticket to avoiding quarantine. Granted there could be enforcement problems as the number of tourists increases, but that's still the answer. Come to Hawaii with proof of a negative test, proceed to enjoy your vacation. Come without it, and either get tested at the airport, or be placed in quarantine.
Hawaii does not have the ability to ban travel to the state. That would be interference in interstate commerce. Like every other state, they do have power to regulate the behavior of people once they enter the state, including quarantine. So when travelers arrive, what they can do is decide whom they can allow to enter without quarantine, and who needs to quarantine. Any testing/scanning program will be built around that.
If were in their situation, I think I would be looking to identify testing entities whose results are considered acceptable. I would also be thinking through some protocols. Is it an virus test or antibody test, and how would my response differ? How recent does the test have to be - and that will likely be different if it's an antibody or a virus presence test. What's the probability that it might be a false negative or positive, and under what circumstances should multiple test results be required to address the false postive/negative scenarios?
These are not easy questions and will require some time to set up and vet. But since Hawaii has elected to control COVID by isolation and quarantine techniques, those are critical questions to answer.