First of all, lets clear up some misconceptions.
Narvik was destroyed as a port for shipping iron ore 1940. For the next four years, until Sweden shut down the ore shipments, the ore was railroaded from Kiruna over Luleå to Oxelösund (south of Stockholm) where it was reloaded on ships and transportet through the Baltic to German ports.
Control of Norway does not give the British access to the Baltic. The southern North Sea remained under German control until 1945, mostly because it is prime mine sea, as is most of the Baltic (there's still about 40-90 000 mines in the Baltic and southern North Sea from ww1 and ww2). The British used MTBs to move agents, evacuate key personell (downed fliers, Norwegian resistance fighters etc) and transport high-quality ball bearings from Sweden during the war, sailing by night at high speeds.
The Swedes and Finns negotiated a state alliance (close to a union, a military alliance and political confederacy) during Spring 1940, but German and Soviet resistance and Finnish revanchism put an end to it (Sweden wanted the alliance to be neutral and that stance to be accepted by both the Germans and the Soviets). With the allies in control in Norway, the German opinion matters far less, and they and the Soviets (who don't want war against the allies or Germany at this point, Stalin wanted the allies and the Germans to bleed each other dry before he intervened) might actually look favourable upon a Swedo-Finnish neutral alliance, as it would secure the northern flank for both of them.
Once the Germans had the control of the French and Belgian iron mines, they were not dependent on Swedish iron ore. Swedish ore was high-quality and was easy to use in the bessemer process to create high-quality steel, but the Germans CAN do without. Sweden needs about 5,5 million tons of coke and coal yearly, and Germany could deliver this 1940-1944, when the western allies could not. Unless the allies can replace this, Sweden will continue to ship iron ore to Germany. OTL, the western allies demanded a reduction in shipping, and Sweden complied, but gave the Germans priority in high grade ore, which made all parts happy.
Allied control of Norway might mean a Swedo-Finnish state alliance, no further Finnish participation in the war and perhaps a France that fights on from North Africa.