BTW, the reason United, LH, OS, LX and AC won't sell US-Europe or Europe-US flights with the long-haul segment on SAS flights is that SK is not part of their transatlantic JV. (
https://www.lufthansagroup.com/en/co...-ventures.html)
I think you can buy a ticket through the JV partners by calling in and get the itinerary manually punched into the system but it will not have competitive pricing.
Once United even refused to reroute me on SK from US. Took a long discussion with a supervisor to finally get on the SK ORD-ARN flight instead of ORD-FRA-ARN with LH.