So, this is sort of a double topic.
A) WI the Beiyang Fleet wins the Battle of the Yalu? The most obvious solution here is to reduce the late Qing's corruption to a manageable level, at least in terms of naval affairs. Perhaps the Dowager Empress retains her interest in the navy, dissuading embezzlement from her pet project? It was a close-fought affair as is, and a few more hits from good shells would have easily destroyed the IOTL badly damaged IJN ships, including the flagship Matsushima. What next?
B) WI the Russian Navy wins the Battle of Tsushima? This is harder. Even if Oryol realizes that it was an IJN ship that she encountered, the Baltic Fleet is still in horrible condition and not ready for battle. Any ideas?