How do I use the 72 hour visa free policy for 5 hour stop in Shanghai?

I have a 1 entry student X to go to China this summer. I am planning to travel in Hong Kong before the program, but the program would only pay for me to fly into mainland, so I am flying into Shanghai Pudong on Swiss Airlines, then I booked a Hong Kong Airlines flight 5 hours later to Hong Kong. 1 week later I am flying back to mainland, so I need that to be my one entry. What do I need to do to make sure my 1 entry is not used when I land in Shanghai to go to Hong Kong? I am only there for 5 hours, so I won't have time to register with a police station or anything, is this ok? Also, I called Swiss Airlines and they insisted they couldn't notify the Shanghai airport that I was coming. Can I still use the policy without this notification? Is there something else I should do to get Swiss Airlines to notify the airport? Thanks!