Interesting if very used question, I'll give some of my musings on this.
From the list you posted, it is easy to scrap roughly half of them immediately.
As you said "Early 1940" I'm assuming 01011940 as the accetable earliest date of entry?
At that point Weserbung is in the future, not the present or the past. Same goes for Fall of France.
Starting from that, there are several alternatives.
Swedish entry into the axis before Weserubung would most likely result in a Axis allied Scandinavia. Mostly since Norway and Denmark would not be able to resist the Axis alone, and would most likely all join together. Geo-politics and all that.
Failing to join after Sweden would only result in massive war gains by the swedes and puppet norways and danish states overseen by a Swedish Axis force, most likely.
That would have serious butterflies all across the field later on, potentially game-changing when it comes to Barbarossa.
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The second interesting possibility that your setting provides for, is the inclusion of either Nat Spain or Swiss into the Axis camp during the early stages or the height of the French campaign.
Imagine Nat Spain joining the axis at about when Paris falls. In that mess they would probably get the N-W Africa and potentially save a portion or the entire France navy. Probably not ofc but it is possible.
The other alternative would be push through both the lowcountries as well as through the Swiss and Italian mountainsides, wouldnt matter much but might save the axis enough time to go for dunkirk? Who knows, but if they do manage to significantly hinder BEF extraction from dunkirk, they might have massive butterflies in the mid-east later on. Potentially not enough for a game changer but definently interesting.
Later entry would def be Turkey after Fall of France, supported by a two prong assault into the Middle East. Most likely the Soviets would not respond to this by invading Turkey in 1940, simply because they werent ready for a war at that point, Turkey or no Turkey. They would give passage rights, intel, and preferrential trades to the allies for sure but an all out invasion of Turkey when your army is entirely unready and the Axis just managed to kick benelux, UK and France out of the continent entirely would be absolute suicide and not what Stalin had in mind, far as I know.
So, pre Weser i'd say Sweden, simply because it in the Axis would save a whole lot of trouble for the Axis.
During FoF I'd say Spain, shortly after i'd still say Spain. But later in the summer or fall of 1940, it shifts to Turkey all the way until 1942 when it probably shifts to Argentina or Mexico, simply becasue it would at least divert some allied units away from Germany or Japan.