It wouldn't be a world war, it would be a civil war at most. There is a large anti-military sentiment in Japan and there were a lot of protests when they changed their constitution to allow them to send troops abroad to aid allies. If they were to launch an un-constitutional invasion of Russia then the government would be absolutely fucked.
And even if they were able to convince the people to support an attack on Russia (it would never happen though), then they'd be the aggressor and Russia would be the one that receives sympathy and support from around the world.
Those Islands are historically Japanese, not Russian though. They belong to Japan, they would just be taking back whats theirs.