By late April 1945 there was direct pressure from the Norwegian Government-in-Exile for Swedish military intervention in Norway.
This would presumably have taken the form of Swedish troops supporting the Norwegian forces exiled in Sweden to invade the country. I expect there were plans and to be fair it isn't that far from the Swedish frontier to Oslo via one of two obvious routes to the north and south. There were only 12,000 or so of these Norwegian "Police" troops and the 20th Mountain Army had a paper strength of 350,000 men so the Swedes would have had to have provided quite a significant additional force.
The Norwegian Resistance Group, Milorg, claimed 40,000 fighters but beyond sabotage and small-scale acts of resistance, I'm not sure how they would have added to brigade-style battles. By all accounts, the 20th Mountain Army wasn't at peak strength or fighting spirit so the question is whether, had the combined Norwegian and Swedish force attacked on April 30th, what kind of resistance would have been put up.
I think it's possible the fighting would have been more between the Wehrmacht and SS (as happened in Denmark) than with the invading forces and you might well have seen street fighting in Oslo with the invading forces and Wehrmacht on one side and the SS (presumably in Akershus) on the other side.
The formal declaration of war had been handed to the German Ambassador in Stockholm on April 30th but there was little he could do as he had lost almost all contact with Berlin at this time.
48 hours after the initial incursion, Swedish forces cross into Norway heading for both Trondheim and Narvik as Wehrmacht resistance begins to collapse.
In the Baltic, Swedish naval activity in the Baltic intensified with German patrol boats coming under fire close to Bornholm and naval skirmishes off the Danish coast. Refugee ships and planes were left undisturbed and some in distress were allowed to land in Sweden.
The same afternoon, a Swedish representative arrived at Montgomery's HQ on Luneburg Heath to insist Norway be part of the capitulation of German forces currently being negotiated. This caused a 24-hour pause as the German delegation, led by von Friedeburg, sought advice from Doenitz.
On the morning of May 5th 1945, after two sharp engagements, both Trondheim and Narvik fell to Swedish forces while by that time Terboven and an SS rearguard were surrounded at Akershus with General Boehme having withdrawn to Stavanger. Doenitz decided to include Norway in the surrender which was signed at 3pm to come into effect the following day.
On May 6th 1945, German forces in North-West Europe, including Denmark and Norway, capitulated to Britain, America and Sweden. As agreed, a Swedish military delegation crossed the Kattegat to Copenhagen and took the surrender of Blumentritt and his command. In Norway, a joint Anglo-Swedish delegation took the surrender of Boehme at Stavanger. In Oslo, Terboven took his own life at Akershus and Vidkun Quisling handed himself to Swedish forces on May 9th hoping for a degree of clemency from Stockholm which would not be forthcoming.