This is a tall order, for sure. I was on a flight from Kahului, HI to Chicago with a layover in Honolulu on August 23 or 24, 1992. There was some kind of a bomb scare in Honolulu and the flight was delayed for a few hours while they searched everyone's luggage. I am wanting more information on this flight, how long the delay was, etc. Is there ANY way I can find it without paying a 24.99 subscription fee to FlightStats...if they even have that info? I believe the carrier was United Airlines.
Your best bet would be local libraries that might have pre-1996 archives of Honolulu Star and/or Honolulu Advertiser (2 newspapers with largest circulation at the time).
Your second best bet would be contacting United Customer service. I would suggest writing them a letter, instead of calling.
Online search does not yield much.
Honolulu International Airport is owned and operated by the State of Hawaii Department of Transportation, and its website has detailed historical information throughout the decades, from 1925 to the present, including a notation of an airport closure due to a hurricane. It suggests comprehensive research and record keeping, and I would recommend contacting the airport directly email@example.com or through the Hawaii DOT Library where an archivist may be able to help location the information.