Is this short transit possible without undertaking a lengthy process to obtain a regular VISA?

As a doctor/counselor I have been asked to accompany an American citizen (who is married to a Chinese national) suffering from fear of flying, departing from PVG Pudong, Shanghai, on 5 April on a nonstop flight to Seattle, U.S.A. For the past seven years she has been teaching business English in China.

I plan to leave Seattle, U.S.A. on 3 April and arrive in PVG on 4 April, if I can process needed permission/VISA prior to my departure from Seattle on 3 April. My time in Shanghai would be less than 48 hours. I am a U.S. citizen.
Thank you.
Mark