I think the easiest route to preventing the war would be to have Russia accept the so-called Man-Kan trade (where Russia would respect Japanese influence in Korea, and Japan would respect Russian influence in Manchuria). That would require huge changes in Russian leadership, though. They were constantly trying to expand their influence in Korea, and they saw no real reason not to try to establish and/or keep Manchuria and Korea in their sphere.
Anyway, assuming the war does not occur for any reason, I wonder if Russia will be stronger or weaker in WW1 (assuming it is not butterflied). On the one hand, the political situation in Russia may be a bit better with no 1905 revolution and no damage to Russia's prestige. On the other hand, Russia does not get the chance to learn from their defeat, so their army may be a bit weaker, their will likely be slower railroad expansion in European Russia.
I think that this is potentially, quite an interesting possibility. Probably the biggest stumbling block would be to try and get Russia to negotiate with 'yellow monkeys' as equals; OTL, Russia was simply not willing to do that until their defeat in the Russo-Japanese War. Having said that, I would be curious as to the effect on Japanese politics; as Korea is placed under Japanese dominion, but with Manchuria ever more securely in the Russian camp, how would this effect the ideology of the Hokushin-ron faction in Japanese politics? This faction's targets are no longer held by a relatively weak power, but is now firmly in the sphere of influence of a Great Power, albeit one of the weaker ones.
WRT the effect on Russia, TBH, everything I know suggests that Russia basically learned virtually nothing, militarily at least, from their defeat in the R-J war (neither did Japan, for that matter). There are, however, certain other implications; this could potentially delay by a fair clip the Dreadnaught naval revolution, which has a huge amount of its impetus in the stunning Japanese naval victory at Tsushima (too, this could also do a great deal to cure the myth of invincibility that was pervasive in the IJN following the R-J war, that arguably helped a great deal in fueling militarism in later years). Politically, on the other hand, Russia may or may not still experience the 1905 Russian Revolution. I, for one, think that it is still likely it will happen; while the defeat in the R-J war is often cited as a cause of the 1905 revolution, I think it is important to remember that the underlying issues and some of the most major eruptions occurred long before the truly disastrous defeats of Russia in the war (ie, Bloody Sunday). The loss of the war contributed to the sense of disillusionment with the Czar among the people, but repression, economic stagnation, and calls for reform had just as huge a role in preparing the ground for the 1905 revolution.