I am a brazillian with a Schengen visa in Basel: can I apply for a Chinese via in Bern (or Zuerich)?

I am doing research at the university of Basel for just one month (Schengen vis -- business VIS). I am a Brazilian citizen and need to go to China on July 30 for a conference. I do not have Swiss permit of any kind. I want to apply for the Chinese visa from Switzerland as there is no time for me to go back to Brazil. Also, is there any expedite service (say, to get it within the same day)?