Osaka - Shanghai - Hong Kong, will this itinerary qualify for the 72 hour visa free stay in Shanghai?

We are planning a trip from Canada, spending 2 weeks in Japan, then fly from Osaka to Shanghai , spend 3 days (less than 72 hours) in Shanghai, then on to Hong Kong (via a connection in Taipei), and finally back to Canada. Does the connection in Taipei cause any issue? Our flight from Shanghai to Hong Kong goes via Taipei, just a short stop to connect flights. Thanks for any comments.