As far as pre94 long guns, the state would have to prove otherwise. But they can trace it back to the manufacturer or look at the FFL books which are still somewhere.
If the store is no longer in business, the FFL records are sent to the ATF and stored in boxes in massive warehouses.
If this is a 1980s purchase, those records were not digitized prior to giving to the ATF. The Feds have been trying to digitize what they have to reduce the storage space required. It's still taking eons to accomplish.
Although the paper records are eventually transformed into digital images, investigators' use of the
computerized system is strictly limited by federal law that prohibits the creation of a searchable
database based on firearms' purchasers.
Gun rights advocates said the system is merely a reflection of what the government requires defunct
gun dealers to do.
I wish the state luck finding that one piece of paper. The records sent to the FBI via NICS for a background check only includes the potential buyer's info. No gun info is sent. That is retained by the FFL on the 4473 and inventory sales records. Once the FFL is defunct, the records go to the ATF. But, the law prohibits the Feds from having a searchable list of gun owners. Therefore, keeping paper records is an acceptable alternative.
If Hawaii Cops want to have the Feds look up the records from that sale in 1980, they are going to have to find the records and manually search each form for the firearm in question.
Not only will that be costly, but the justification would be pretty weak IMO. If the only crime committed was failure to register, that misdemeanor can be remedied by simply registering it. If you don't want to, then that's between you and the AG to figure out. A receipt is not the only way to prove you owned it before 1994. A photo of you holding it, someone who was with you when you bought it signing an affidavit, or any dated document you recorded the serial number on before 1994 should be sufficient.
HPD doesn't ask for receipts for out-of-state guns. I really don't see them pushing the issue without some evidence to contradict your story.

MARTINSBURG, W.Va. — Millions of firearm purchase records, potentially critical to tracing
guns used in crimes, languish here in scores of cardboard boxes and shipping containers
awaiting processing at the government's National Tracing Center.
Officials estimate that 1.6 million paper documents and other records arrive every month
from defunct firearm dealers who are required to ship their business records, some barely
discernible, to this Bureau of Alcohol Tobacco Firearms and Explosives facility for eventual
inclusion in a digital repository.
Up to 50 times a day, document examiners comb through everything from 1970s-era microfilm
to hand-written cards in an effort to satisfy sometimes urgent pleas for assistance from law
enforcement agencies from across the country, ATF information specialist Neil Troppman said.
https://www.usatoday.com/story/news/nation/2015/10/27/firearms-national-tracing-center-atf/74401060/