I want to fly into Shanghai from Japan (UK citizen)

with the ultimate aim of getting the trans-Mongolian express from Beijing. Therefore I wish to enter and leave from two eligible transit ports (the airport and train station in Shanghai) and I will have confirmation of onward travel out of China within the time limit. However, the onward journey out of China involves changing trains in Beijing to travel to Mongolia. How does this impact on the the restriction of not being able to visit cities outside of the administrative regions? I technically don't want to visit Beijing, it just happens to be where I need to change trains for my onward journey? Does this still constitute part of my onward travel or would I be classed as going out of the area and therefore need a tourist visa? Thanks