I just bought a used .22 pistol that had the original 1948-dated Territory of Hawaii registration paper in the box. So, yes, pistols did have to be registered, even before HI became a state.
Before the two-week waiting period was instituted, I remember that you had to take the S/N of the pistol down to HPD, you filled out the paperwork and they gave you the form right then and there. You took the form back to the gunshop, completed the 4473, then returned to HPD with the completed permit and they registered it to you then and there.
Can't help you with your aunt's memory though, but she would have had to get the permit from HPD in the first place. If she didn't register it afterwards the cops would have called her about it.