Applying for tourist L after holding Z for many years

I have worked in China as a university professor for many years but have been told my contract cannot be extended and I must retire due to my age. My Z expires July 10. However, I would like to remain for tourist purposes for some weeks before leaving. I am planning a brief visit to Singapore from June 12. Will I be able to apply for a tourist L there to return to Beijing. Thank you
Geoffrey Murray