If the Japanese are only attacking the Soviet Union there is no way the British will declare war. Given their situation in North Africa and Europe they have nothing to gain and a lot to lose. With the Russians already fully committed to fighting the Germans a declaration of war will not bring them any new allies. While at the same time putting their Asian colonies in serious danger.
I can see a lot of pressure for this, both from Stalin and from many elements in Britain. Not just internal politics. The nightmare other than the Soviets being defeated is Stalin making a separate peace. [Which would be very difficult since Hitler would never agree if he thought he was winning but that wouldn't be clear at the time]. After all, reluctantly it may be but we did declare war on Finland and they had a decent reason for fighting the Soviets.
The empire, with some preparation and careful planning, would be pretty safe against the Japanese. [Whether we would have careful planning with Churchill in charge might be a different matter.

]. Also with the views at the time I could see a lot of people vastly underestimating the Japanese.
The other concern would be the vulnerability of the Dutch colonies, which would be far more difficult to defend. If we could get a cast-iron guarantee from Roosevelt to defend them from a Japanese attack the idea would be viable. [However between his internal problems and desire to have anyone else do the work that could be a serious sticking point

].
Obviously the US is not going to go to war just to defend the Soviet Union. I doubt it would even be cause for sanctions. If in this time line the Japanese choose not to enter Indochina the US might not freeze their assets or issue an embargo.
I'm pretty certain that Roosevelt would tighten any embargo but this would be after the one imposed for invading French Indo-China, the southern half of which was taken over in ~June 41 I think, i.e. before the POD. Since he's desperately trying to prevent the anti-Nazi powers collapsing and there is already anger at the Japanese expansionism and their just attacked another power.
Steve
PS One other point to consider. If the Japanese get into a serious rumble in Siberia, both tying up forces and losing prestige, could they fail to cower Thailand? That would make things a lot easier in defending SE Asia.