The most direct way to non-Russian majority Kaliningrad/Königsburg would be Stalin being paranoid in a different way in 1941. If the Soviet Army is prepared for the assault at Barbarossa (or even launches a preemptive attack a few days before Barbarossa commences) it is not unlikely that Germany collapses by 1943 - or even earlier if the generals turn on Hitler earlier. The USSR is not feeling a need for bloody revenge but still wants to de-fang Germany and add a line of buffer states to the West; in the occuped East Prussia, a communist coup brings people to the power who are closely aligned with Stalin. While not being formally annexed to USSR, the People's Republic of Prussia (OOC: or will it be called something else entirely?) is even more a puppet state of USSR than GDR was IOTL; so far that the capital city is renamed Kalininstadt, and is often referred to as Kaliningrad in Russian - so often that the usage becomes internationally accepted.
By the 1990, though, the Prussians are tired of being USSR's lapdogs; they see Polish People's Republic being the "window to the West" and get Soviet money and ressources as window dressing, while Prussia becomes an impoverished backwater only held up economically somewhat by the Soviet navy and strategic air bases. Following example of Lithuania in 1991, Prussians take to the streets; the Soviet leadership, preoccupied by unrest elsewhere in the huge empire, on a reform course and not being able to roll in with the tanks without losing face, has to accept a new, far less Soviet friendly government of Republic of Prussia. Kalininstadt is renamed back to Königsberg, but both names continue to be used colloquially well into the 2000s...