I looked up a thread on this issue.

What is an FFL?

I have the safety course done, and I have owned other handguns

How do I go about purchasing a handgun elsewhere cause no one carries it on the island

Find a dealer anywhere in the USA online and purchase it from them. They will have to ship it to an FFL (gun shop) here.

Try GunBroker.com and search for whatever you are looking for. When you complete your transaction they will ask for the FFL information to transfer the firearm here. Take warning. Make sure you can obtain a pistol permit before you buy it. Once you purchase it and it's on its way here you own it. If by chance you are unable to complete the transaction, I'm sure the LGS will sell it for you on consignment.

I'm sure plenty of vendors here will do the transfer for you. Contact them and they will explain it better than I.

FFL stands for federal firearms license.
Generally referred to as firearm stores. 

Easiest way is to go to a firearms shop and ask if they can bring in the firearm for you. 
You pay them and when it comes in you do the Hawaii registration aspect.

A firearms store can help walk you through the process

Find a dealer anywhere in the USA online and purchase it from them. They will have to ship it to an FFL (gun shop) here.

Try GunBroker.com and search for whatever you are looking for. When you complete your transaction they will ask for the FFL information to transfer the firearm here. Take warning. Make sure you can obtain a pistol permit before you buy it. Once you purchase it and it's on its way here you own it. If by chance you are unable to complete the transaction, I'm sure the LGS will sell it for you on consignment.

I'm sure plenty of vendors here will do the transfer for you. Contact them and they will explain it better than I.

FFL = Federal Firearms Licensee.  They are licensed to conduct interstate transfers of firearms, most importantly handguns. 

One very good way to know if you will pass the Hawaii firearm background check is to apply for a long gun permit.  No need to provide any specs on any long gun -- the permit is good for any number of long guns you buy for 12 months. (this might change one day, but for now, this is the law)

Once you have the long gun permit, the pistol permit should be a cake walk.  Wait for the gun to arrive at the FFL you selected, and go inspect it.  You normally get 3 days after FFL receipt from the seller to inspect and return it.  Just make sure it's the gun you expected, and that it's in the condition advertised.  You can look, but you can't shoot it during the inspection.

Once you've verified the gun is what you paid for, take the vital stats (make, model, serial #, caliber, action, barrel length, etc) to apply for the permit.  When you apply, you list the FFL's name as the seller or transferor.  They are transferring the gun to you, not the person/business who sold it to you.

After waiting 2 weeks from date of application, pick up the permit.  Then pick up the gun.  Then take your copy of the permit and the gun BACK to the police station to register it.

Many threads on this forum on how to buy and register guns.  If you get confused or need help, just ask.

make sure the handgun you are purchasing is legal to own here in Hawaii--no shockwaves, ar/ak pistols with detachable mags, no 10/22 chargers, uzi pistols, etc.

make sure the handgun you are purchasing is legal to own here in Hawaii--no shockwaves, ar/ak pistols with detachable mags, no 10/22 chargers, uzi pistols, etc.

Usually the sellers will know, and the FFL will definitely know, what's legal.  It's wise to ask BEFORE committing to purchasing, though.

The most common issue is mag capacity limits here.  Some sellers can swap mags to be compliant, or you'll have to have >10rd mags blocked by an FFL.  The alternative is to buy the gun without mags if it's a bargain, and then find compliant mags separately.  It really all depends on how willing the seller is to accommodate you and our messed-up gun laws.   

Another option is to ask the store here to special order the firearm for you from the distributor.  Most stores can get just about anything.

What are ya looking to get? 🤔

As for options for getting exactly what you want, I’ve done both the order and FFL transfer and special order through local gun shops. Overall, both good methods. With SHOT going on now, expect to wait a bit longer for special orders.