Transit SAS to Asiana - need to check out luggage?

Hello,
I plan to fly from Copenhagen (Denmark) to Seoul (South Korea) in April. An option is to fly via Shanghai. Will I need to claim my luggage at Shanghai and re-check it or can it be checked all the way through from Copenhagen to Seoul? Flying SAS and Asiana or SAS and Korean Airlines.
Also, do I need to apply for a transit visa?
BR
Louise Broge