I don’t have experience with SAS, but fly with a guitar all the time and rarely have issues taking it on board, although it’s definitely over the limit size-wise. Having *G status does help.

Some airlines are more instrument friendly than others. United have been bending over backwards since the “United breaks guitars” video, to the extent of putting crew baggage in the hold so my guitar could be in the cabin.

If it’s a cheap ticket, just buy another seat as perfect insurance.

If the check-in agent brings it up, this sentence has worked wonders: “I have to do what you tell me, but the cabin crew on (insert airline here) are always so wonderful. Could I please take it to the plane, we can always gate check it if there’s really no space.”