It's funny how you bring up the Wokou as an example of Qing ineptness.
Wokou raids were at their high between 14-16C, when the Ashikaga Shogunate was powerless over Japan. A lot of the pirates usually lumped together as "Wokou/Wakou" were actually Chinese, and their constant raids were more of a symptom of Ming losing control on itself rather than Japanese military strength. Korea led a successful expedition to Tsushima in 1419; Japan under Toyotomi got their internal problems sorted out and largely stopped the pirates; Qing fortified the targeted areas like Fujian and had little problem defending the coastline.
Now, let's get into a fun historical imagination. Could 30K Western military successfully defeat even Korea in 1650-1700? (Becauase that's the time frame of OP's discussion) For the sake of argument, I'm going to ignore the naval transportation problems because that's basically what we're given in the game. Korea in this time frame was fielding ~45000 standing army. Further, not only that the gunpower weapons were already being widely used for centuries, they also had the knowledge of Western military technology because they had Dutch advisors in weapons manufacturing and military training in the capital. I'll let your imagination run wild. I'd say probably, but not in a roflstomping way.
