Aloha Texan,
You don't need to worry about traveling with an unregistered gun. Registration is a requirement only to possess the gun in Hawaii. The airlines do not monitor, enforce, or even care about registration.
Place the gun in a hard-sided container. Lock the container. Do NOT use a TSA lock. You can either check that container, or place it in another bag and check that. When you check the bag, tell the friendly airline clerk that you have an unloaded firearm. A few things will happen:
1. You will be given a small form to fill out and place inside the gun case.
2. You will be taken out of line and introduced to a friendly TSA agent.
3. Under your supervision, the TSA agent will ask you to open your gun case, and they will inspect the contents.
4. The TSA agent will watch you close and lock the case.
5. Your bag will be placed on the conveyor belt, and you will go on with the boarding process.
That's it!