The Chinese being a republic since 1911 is different than their modernisation, since a lot has to do with resentment toward the Qing that wouldn't necessarily exist under an ethnically Han dynasty, be it the Shun or whoever won after the fall of the Ming. So much of industrialisation and modernisation is based on Europe's example--look at Thailand and Madagascar's example for modernisation attempts.
I think a good POD for that might be continued Japanese expansionism, like Hideyoshi's conflicts in Korea and his plans for Taiwan and Luzon. I don't know if a Toyotomi shogunate would necessarily lead to this, but any way to shape the Japanese way of thought as looking outward could lead to this (Mongols, Kenmu Restoration, etc.). If China and Japan end up like the French and British in Europe, then I'd assume they'd end up "joining" the Western world, since the competition would make them adopt what was best. And at times, they'd be the ones innovating. Such as the fact that the late Sengoku era had Japan becoming one of the main manufacturers of muskets-the "Tanegashima" (or hinawajuu) is one of the major designs of matchlocks, and Japan made a ton of them. And China is capable of the same thing, and I believe the Ming/early Qing did similar things which hints to their capability. If Japan and China end up as bitter rivals, then that creates a lot of competition. Taiwan and the Philippines might be areas of conflict, and also Siberia and most exotically the West Coast of the Americas, where they'd come into conflict with Spain but also be able to absorb more Spanish influences as Japan historically did. Korea is another flashpoint, since geopolitically, Korea resembles 19th century Belgium and might change it's allegiance between China and Japan as circumstances require but as Belgium did, itself be a center of innovation. Industrialism-wise, Korea is wealthy in resources, and going back to the Belgium comparison, Belgium was the second country to industrialise after Britain.
In short, it's definitely possible.