Tourist visa is OK after my studying one expires

Currently I have a resident permit for China because I have been studying in Shanghai for 10 months. My visa will expire om 31 December 2014, but my return ticket is scheduled on 12 January. Can I go to hong kong on 31 December (when my visa expiree) to apply for a tourist L so I can go back to China in the next few days? How long will it take to get it and what is the shortest time? Thank you