Essen performs epic fail. Sweden enters the war and grabs Åland islands and the parts of Finland that they can get without actually fighting, probably by advancing south along the Gulf of Bothnia coast. They recruit and arm all the Finnish volunteers they can, and occassionally do a pinprick attack and generally speaking look scary and force as many Russian troops to twiddle their thumbs in Finland as they can. Eastern front collapses slightly earlier, US entry to the war is delayed, Sweden gets out of war before US declaration of war, or at least before US gets around to declaring war on German allies. Sweden gets the Åland islands and a sphere of influence in Finland and Baltic states, minor gains, but they got them without spending enormous amounts of blood or treasure. Russia collapses into revolution, Finland makes landgrab towards White Sea, they have much better and larger army than OTL. Western front will still have something like the spring offensive before US enters the war and it will still fail. Moving towards WW2, Stalin does not necessarily go after Baltic states or Finland if a fight and western intervention is a real possibility. If something like WW2 still goes on, maybe the Swedish block could be enticed to join the de-nazification of Europe when US joins the war again?
Sweden is a stable constitutional monarchy without enough power to really oppress anyone, so strong Swedish influence on newly independent states is probably all for the good. If Stalin leaves well enough alone, maybe the Nazis manage to annoy the Baltic states enough that when their fortunes turn, they'll want their pound of flesh and drag Sweden in with them. Especially if USA promises some sugar.
WW1 military tech favors defender, a lot. So, have local Finns to scout out Russian troop positions and fortifications. Gulf of Finland is probably about equal mixture of mines and water, but grab one or more of the lightly defended port towns on Gulf of Bothnia. Fortify and supply via sea. Build an armored train or something, and if there is a lightly defended rail link, attack and grab and fortify next railhead. Supply by rail. Finland is pretty big place, actually, so any enemy counterattacks almost have to come along the rail network. Push towards St. Petersburg, Russians have to defend. Sit pretty, and try and tie up as much of Russian army you can, while Germans fight on eastern front.