If the British plan of 1939 to invade Narvik and march overland and occupy the Swedish Iron Ore mines in the north of the country had gone ahead things would undoubtedly be different.
Fortunately the Finns, aiding who in the Winter War was the excuse for this debacle, made peace with Russia and the plan was shelved.
Now, if Britain had actually succeeding in invading any Swedish territory, no matter how peripheral, the prospects would be much better for Sweden to join the Axis
voluntarily which is a hell of a much better scenario from Hitler's point of view.
Sweden OTL was on the knife edge as it was. I believe there were a great many Swedes who would strongly oppose being openly allied with Hitler (many of them were much more willing to be a friendly neutral as OTL). However there were pro-Nazi Swedes surely, and there were surely more who just did the math, looked at the maps, and figured the German side would be the smart one to be on. Things I have read suggest to me the King of Sweden rather preferred the German side himself, particularly once the Soviets were on the other side. If that is a slander of that monarch I apologize, but at any rate I gather he was rather more open to German friendship than the Kings of Denmark and Norway--the latter of course becoming an active leader of armed resistance, the former taking rather heroic risks to protect his people (of all persuasions and ancestries). Anyway, once the Russians attacked Finland the Swedes were generally quite hostile to the Soviets and friendly to whoever (besides themselves) helped the Finns. Once Hitler was no longer allied with the Soviets, the nation was in a rather delicate balance, and it was neutrality, not a pro-Allied stance, that was favored.
Of course had Sweden somehow tipped in a pro-Allied direction, they'd have been in big trouble at least until very late in the war. (And then, what help and hope they'd have, other than the general state of decimation and distraction of the German war machine, would have had to come from the East, from which direction it would be least welcome).
So,
if the British plan to secure the Swedish iron fields had gone forward, I can see the right-wing forces in Sweden prevailing politically enough to actively throw in with Hitler, especially that early in the war. Many who might have much preferred not to be Hitler's ally would probably go along quietly both for patriotic reasons and out of a sense of self-preservation. Not to mention that after Barbarossa, they'd be quite free to help the Finns and Hitler, if he was half-smart by that point, would probably assign what token support Sweden could give to his total war effort to that sector--"Go save Finland and take as much from the Bolsheviks to the east as you can with their help!"
Of course the first Swedish priority would be to try and drive the British out of their own country and help the Germans take away their base at Narvik too. Without the Swedish iron, Hitler would have been hurting, so it would be a German priority too.
Voluntary Swedish help would be much more valuable to Hitler than trying to occupy the place against their will, and as things were OTL he got a certain amount of that for no cost at all. A Nazi-allied Sweden might need to police itself rather heavily--I daresay there would be
some resistance--and that might even come to be a bit of a drain on even German resources, especially as the war was not going in his favor and many Swedes might be refiguring their options. (Including people in the military and police!) But even then not nearly as much as the cost of a hostile occupation would be from day one, even if the Germans could magically march in against no resistance at all from Sweden's own forces.
I heartily endorse the posts about the abuse of the term "ASB" by the way. At least once so far (and I've only been here since last summer) I've seen it used in the first post on someone's thread coupled with an appeal to moderators to move the thread forthwith. That thread's OP contained nothing that was in any way fantastical, silly, or to my mind even the least bit improbable. Obviously this first poster and I disagreed strongly, but it was an essentially
political disagreement, having nothing to do with anything going even against "human nature," let alone the natural kind of nature.
If we allow standards like that to prevail, all threads would belong in ASB. If we do it inconsistently, it is arbitrary at best and systematic political bullying at worst.
I think this particular OP here is quite improbable, but only because one assumes Hitler had a lick of common sense. And only because he was in fact able to get a lot of what he wanted from Sweden without threatening them at all (save insofar as his actions elsewhere were inherently an implicit threat.) If the Swedes, given their position, had been foolhardy enough to defy him once he'd occupied Norway, I am sure he'd have invaded quite quickly, pre-existing plans or none.
Perhaps, had the Swedes had more foresight and had not some of them been bewildered enough to think Hitler's rise might be a good thing, they could have changed the picture for Norway and prevented that nation from being invaded successfully. If those two prideful neighbor nations had been cooperative enough in advance, that is.
If that help were not enough to save Norway, or at any rate not all of it and the Germans retained a foothold there, then the Swedes would be facing a very nasty fight indeed, and there would not have been a whole lot the British could have done to help them.
I am afraid there was really nothing the Swedes could do for Denmark, save try to prevent it from becoming a war zone by avoiding fighting the Germans completely. Which is of course what happened OTL.