If your stay in Hong Kong is less than 14 days, the China embassy in Singapore can issue Hong Kong visa to you, it takes 4 working days, if you want to stay in Hk for more than 14 days, your application should get the approval of Hong Kong immigration Department, so it takes about 1 month. You can go to China embassy in Singapore directly to apply for HK visa. Your original passport don't need to be left for Hong Kong visa application. The photocopy of your passport is required.