Basically, what others have said. You're flying domestically. If you were coming in from any of the dozen countries from which there are direct flights to Honolulu, then yes, you'd be sent through immigration. (You could, for example, fly MNL-HNL direct.)

As far as I'm aware, there's no way to get to immigration under normal circumstances except by arriving internationally. I suppose you could ask a Wiki-Wiki driver to take you there and see what they say, but even if they did, you'd have to make up some story for the immigration officer - and persuade them to give you a stamp, since like all points of entry, they do that somewhat inconsistently.

I've done 32 international trips (12 returned via HNL) in the last ~9 years, and have 13 entry stamps to show for it (of which only 2-3 are "HHW").