Shipborn supply can come through Narvik or Trondheim, both are connected by railroad to the general Swedish railroad network. Before the 20. Gebirgsarmee started retreating from northern Finland, the German garrison in Narvik is meagre. Sweden can probably take it with a dedicated push.
Sweden has a substantial mine sweeping capability at the time (since the Baltic is mine heaven), with 43 dedicated, purpose-built minesweepers, 34 patrol boats with mine-sweeping ability and about 100 auxiliary minesweepers (converted trawlers etc) - if you add the British sweeping from the other side to open the sea lanes and control the southern North Sea (which will cut the German troops in Norway off from supply), I think it can be done rather quickly. It requires the western allies to dedicate substantial naval and air assets to controlling the waters to be swept though.
Sweden entering the war, the British and Americans taking control of the southern North Sea and the Finns switching sides will also isolate the 20. Gebirgsarmee in Finland - it will run out of supplies trying to hold Rovanieme or another Finnish port (retreating to Norway is not an option if the Swedes have taken Narvik).