US-Shanghai-Taiwan

Because of the good ticket pricing, I am planning to book two separate round-trip tickets:

Detroit - Shanghai Pudong
Shanghai Pudong - Taiwan

Since I will probably only stay at the Pudong airport for few hours to get on the next flight to Taiwan, I think I should be eligible for the 72 hr free visa transit policy? If so, would I need to prepare any document or apply for any free visa permit in advance? I will have the confirmed ticket with seating from Shanghai to Taiwan in hands. Thanks!