Less than 24h stopover - transit visa? luggage storage?

Hi! I am from Denmark, so from one of the eligible countries for transit visa.

I am an exchange student in Shanghai, who plan to travel outside of China in July. I will leave my luggage in Shanghai since my flight back to Denmark is departuring from Shanghai.

So, my final itinerary will be: Singapore - Shanghai - Copenhagen. I have a stopover less than 24 hours in Shanghai before my final flight to Copenhagen. Can you assure me that it is possible for me to leave the airport and collect my luggage left at a friend's place and return for my final flight within 24 hours? My other option is to store my luggage in the airport during my travels outside China in July, but this is very expensive... Am I assured a transit visa with all necessary documents? Do I even need to apply for one?

Looking forward to a clear answer! Thanks!