Can use 72hr per city like Shanghai then use another 72hrs Bejing? I am a Canadian?

I wasn't aware of the visa till now. Its almost too late to apply for entry permit to China.
I booked my stay for 5days in Shanghai as there is a layover.

Now, i am not sure what to do?
I don't have an entry permit..but can use the free 72hours free transit per city to avoid having an entry permit?