Flying from New York - Seoul

I am going to fly from NY to Seoul with a stopover in Shanghai.
As I wish to see the city for at least a day, I am planning to do this itinerary as two different tickets (ie. NY - Shanghai, Shanghai - Seoul). The time between the two flights will be less than 72 hours, but it worries me as it is not technically a transit, but rather two different flights.
Does anyone know if this would still work?