Sweden would want to occupy Åland and might even try it, but would it lead to Åland becoming a part of Sweden, even de facto if not de jure? I find it unlikely.
I have crossed swords with von Adler over this in other threads, and basically I just don't believe the Swedish government would be united behind an occupation scheme that would risk making the nation a combatant in the world war.
1918 offers a good comparison. The Swedish Navy had a presence in Åland and the plan to take over the islands was approved by many in the parliament, as well as the royals, but when it came to a showdown with a major power (that time Germany, supporting the Finnish [White] government), Sweden backed down to stay on the safe side.
There were pre-WWII plans for a joint naval defence of Åland, but during the OTL Winter War they were not realized. They were dashed together with all other binding measures of open support to Finland. Which in Sweden proved (domestically) politically impossible, as desperate Finnish envoys found out.
After the fall of Finland into Soviet sphere or actual annexation is fait accompli, would Stockholm really have the political will and unity to challenge a major power and risk war, reversing a hundred-and-thirty-year tradition of neutrality? Make that two major powers if Germany still (at least ostensibly) stands behind the MR pact and openly rebuffs the Swedish plans.
What did Finland do whan Stalin turned on the heat? Really contemplated about doing things like handing over some of its national territory or otherwise undermining its sovereignty. Facing the the prospect of being next on the butcher's block, would Sweden actually move to occupy land that Stalin already claims as his own?
I can well imagine the political stress the Swedish government would be under. "Not making any rash moves" might well be the order of the day.