I had a similar situation, although mine was even more involved. The handgun I had was registered to my father in California because I was a minor when I first bought it there. I called HPD a few times about it, called CA people, and the airlines. I didn't want to make a mistake and get in trouble. I thought I would have to transfer ownership in CA first, then bring it or have some kind of paperwork proving it was mine, etc.
It wasn't until a lengthy conversation with HPD that I felt better. They told me, since different states don't share info, the only thing Hawaii cared about was who was responsible for the gun once it was in Hawaii. I bring it into the state, I register it, that's it. You don't need to prove who owned it previously, when it was purchased, nothing. The airlines didn't need any paperwork and neither did HPD. I showed up at HPD, filled out the regular paperwork, and that was that. It was way easier than I thought. I've been in line with several other people registering out is state guns and their experience was the same as mine.