Few itineraries expose the strange geometry of long-haul travel quite like the journey from Honolulu to Malmo, a routing that has no nonstop option and instead demands a thoughtful choice of connecting hub across the Pacific and then Europe. There is no business class from Honolulu to Malmo that doesn't involve at least one, and usually two, stops, since Malmo's Sturup Airport is a regional field served primarily by SAS and its codeshare partners rather than long-haul carriers directly. The practical fact worth remembering: your best bet is routing through a US mainland gateway to Europe, then down into Copenhagen (a short hop or even train ride from Malmo across the Öresund Bridge), which is precisely why SAS, Lufthansa, and KLM dominate the routing options here.
Having flown this corridor several times, I've come to favor connecting through Frankfurt or Munich on Lufthansa, especially now that Allegris business class is rolling out on select long-haul aircraft, offering more privacy and configuration options than the older business product. KLM's World Business Class via Amsterdam is a dependable alternative, with their 787 and A330 cabins offering lie-flat comfort and a smooth connection bank into Copenhagen, from which the train to Malmo takes under 30 minutes—genuinely faster than waiting for a puddle-jumper flight. SAS itself, once you're within their European network, offers a comfortable if more modest business cabin, and their Copenhagen hub is worth lingering in if you have a few hours, particularly for the lounge showers after the long haul from Honolulu.
My insider tip: book the Honolulu–mainland segment as a separate positioning flight in premium economy or even first class using miles, then start your business class ticketing from a West Coast gateway like Los Angeles or San Francisco, since award and revenue pricing for HNL-origin business itineraries to Scandinavia are often inflated compared to mainland departures. Given how thin and seasonal this market is, with softer fares typically appearing between May and September, setting up automated fare alerts is the smartest way to catch a rare, well-priced business class release before it disappears.