Should I send the application fee with my application at the same time? Any benefits?

I have travel ticket from US to Hong Kong and Hong Kong to Shanghai leaving US on September 3rd. I do not have a HK visa yet. The chinese consulate in NY told me to contact HK directly. I was told that I need to send my application to honk kong office. I am a US perm. resident with a Nigerian passport. What steps can i take to ensure i receive the visa before September. I understand it takes about 4-6 weeks which is really close now. Can HK embassy send me express mail once the entry permit is ready? or what suggestions do you have?