I’m certainly no expert but I get the impression that Sweden as a whole wasn’t too keen on the Nazis, especially after watching them trample the sovereignty of their Scandinavian neighbors. Sweden was really in an impossible place, being surrounded on all sides by Nazi-controlled territory. I reckon they figured their best bet was to avoid an ugly fight and occupation and acquiesce to German trade and transportation demands. I think it’s very telling that as soon as the tide started to swing against the Axis, the Swedes were entering talks with the Allies about liberating Denmark, even though they were still surrounded by the Nazi empire.
Very few Swedish volunteers joined the German Army or Waffen SS. Many fought with the Finns again in the Continuation War, but Swedes in the Wermacht/SS were very small relative to other nations like Norway, Belgium, France, and others. I wouldn’t advocate any A&A trigger for Sweden to join the Axis. I haven’t read anything that indicates a serious leaning toward the Axis. But again, I’m no expert on Sweden; I would love to hear dissenting opinions.