This is all pretty entertaining. If we were invaded, firearms registration records would be the least of our worries. The idea that an invading force will track you down that way is just FUD used in movies for dramatic effect. But since this is a hypothetical, I'm pretty sure things would fall in line with what Q said. It won't be about who has guns, but who is willing to take them up and become a threat.
In reality, Hawaii has never been a target for invasion and the likelihood of it in the modern age of warfare is nonexistent. Our location being of strategic value ended with the age of sail and the only natural resources we have is fresh water and a little agriculture. Just think of the logistical requirements for an invasion then occupation and you'll see it's never going to happen.
There's a twist to the plot if Hawaii were invaded compared to Calumet, CO, in the movie
Red Dawn. Hawaii has a pretty substantial military presence. Personnel, arms, ammo, heavy weapons, protective gear, high tech weapons, comms, Intel, and other in-place supplies.
Add to that the civilian population, law enforcement, the weapons, ammo, and gear available from those sources, and the vast Naval assets in port, deployed, and in transit, I believe any force that attempted to invade would have to catch our forces by total surprise. I hope we learned some valuable lessons from the Japanese attack on Pearl Harbor that will give us much earlier warning than we had on that day.