If you are not transporting your guns either through a house hold goods shipment, or bringing them on the plane -- you will be shipping through an FFL. You would be required to have proof of that NRA first steps course, however, that may be insufficient, since first steps is only 3 hrs (and does not cover Hawaii laws).
When I do the training for students, we make sure that the appropriate # of hours of classroom (4) and range (2) is documented on the sheet, since that is what is called out in the law.
So it comes down to this:
1- If you transport the guns in, I would say you are good to go, or;
2- If you are shipping through an FFL I am sensing probable issues with your handgun safety class.