How can a US Citizen visit Shenzhen for 2-3 days?

My wife and I plan to fly from Ireland to Auckland via a 3-day stopover in Hong Kong. We would like to visit Shenzhen where we have a nephew working as a teacher. I have a Canadian passport and my wife a US passport. From this site my understanding is that a US Citizen cannot gain entry with a Visa On Arrival and may infact be fined.

Is there a process for a US citizen to visit Shenzhen for a short visit?