In 1892, while the future Nicholas II of Russia was engaging in his world tour/ Trans-Siberian railway inaguration ceremony he stopped in Kyoto- where one of his official police escorts, one Tsuda Sanzō, had a bout of xenophobic patriotism and tried to chop Nicholas up with a sabre.
Fortunately for Nicholas and Japan, and unfortunately for Russia, the first blow was only glancing and the second blow was parried by his cousin prince George of Greece.
So let's suppose that Tsuda is more successful and kills both Nicholas and George before being apprehended.
What is the realistic/plausible short term outcome?
The Transsiberian Railway is not yet built so Russia has a very limited ability to project land power to East Asia. I think it's garrison in the Transbaikal and TranAmur amounts to perhaps 60,000 regular and Cossack troops- perhaps a quarter of what the Japanese army can raise. They can be reinforced, of course, but marching from Chelyabinsk on the Ural mountains to the Pacific is quite a Trek.
On the other hand, the Russian navy, even the far east flotilla, ridiculously outmasses the Japanese fleet. 1892-1894 is precisely when the Japanese navy underwent massive expansion (and the navy it used during the first sino Japanese war was still miniscule by European standards).
So the Russians can’t exactly invade the Japanese home isles, Probably not even Hokaido, but they can prevent the Japanese from invading the Asian mainland (maybe not Sakhlain). They can probably capture the Kuriles, and perhaps Tsunshima and Okinawa.
They can also try to impose a blockade on Japan, or at least on it's primary ports and they can launch terror bombardments on coastal settlements lacking strong defenses (most of them). They might even be able to force the defences of Yokohoma bay and shell Tokyo. They would be running short of shells, and coal, pretty quickly though and would find it difficult to operate exclusively out of Vladivostok.
Operating out of Korea's and China's treaty ports would eventually raise international eyebrows but I can’t really see any of the Colonial powers, or even the United States, openly intervening on Japan's behalf. On the other hand, long-term interdection of Japanese trade is going to make some capitalists in San-Francisco very unhappy- at some point the United states is going to try to mediate and settlement.
There's also the question of what Russia can possibly hope to achieve, realisticly, besides revenge and upholding their sacred honor. I mean, occupying and Ruling Japan is obviously out.
So way I see it it could go one of six ways:
1. Tsar Alexander takes a deep breath, realizes he can’t really gain much out of a war and presents Japan with a list of demands they can probably accept. The Kurile islands and a massive indemmity, enough to cripple the Japanese military buildup until the Trans-Siberian railway is completed.
1a. When the Tonghak rebellion breaks out and China sends troops to put it down the Japanese government lacks the ships or confidence to credibly challenge China for naval dominance of the Yellow sea. China transforms Korea into a de-facto protectorate and may yet undergo sufficiently successful reform by the time a WWI analog breaks out to evade
1b. Japan goes to war with inadequate resources and the war in Korea grinds down into a stalemate similliar to Japan's first invasion of Korea under Hideyoshi. 1c. Japan still goes to war, (possibly it waits a few more years), and still wins, though less spectacularly than OTL. When it does, however, it faces an unpleasant surprise- Russia intervenes on China's side and forces them to withdraw to the home isles sans any territorial gains or an indemmity.
2. Alexander demands too much (Tsunshima, Okinawa or even Hokaido), or the faction ridden Japanese government is unwilling to submit to gunboat diplomacy. War ensues.
2a. The war is expensive for Russia and the small Japanese fleet surprisingly adroit at raiding Russian colliers. Japan is devastated but preserves independence and all of it's territory save the Kuriles.
2b. Russian marines kick ass- Japan loses not only the Kuriles but Tsunshima, sado, and the Ryukus as well. Japan desprately seeks allies which will aid (and subsidise) a future war of revanche, and does not need to seek far.
2c. With his coastal cities in ruins and his people starving (1892 Japan did not depend on rice imports as much as 1942 Japan but was not self reliant) Meiji has no choice but to surrender. Japan loses the Kuriles, Tsunshima, the Ryukus and even Hokaido outright and the rest becomes a defacto protectorate, with it’s army relegated to internal policing (which is badly needed. Defeat leads to many revolts), it's navy permanently dismantled and it’s foreign affairs conducted exclusively through Russia. Russia realizes, however, that Japan is a permanent achiless heel. It reorients it's foreign policy away from the Balkans, The Middle East and Central Asia, and seeks to reach an entente with Britain while simultaneously seeking greater political control over lands lying between Japan and the Russian mainland (Like Korea. And Manchuria)
Which outcome seems most likely?