Yes, use a search engine, a slight bit of Chinese and apply directly. Don't ever use a recruiter.

Wikipedia has lists of all the universities within a certain province, you can use that as starting point to find websites or at least, the names of universities. If you are slightly China savvy, you may know of quite a few smaller cities that are untouched gems.

Several universities have web pages, with HR details. However, the English sites tend to be poorly maintained because of they are of little importance when they find teachers who already live locally. So look on the Chinese pages, find the contact details of department heads and apply directly. The worst that can happen is that you get no response.