Usually the flight crew makes special arrangments for you to get off first in case you have a very short connection. I've been on delayed flights into CPH where we were specifically asked to remain seated and allow passengers connecting to PEK and some other destination to get off first so that they may catch their flights.

Also if you are in such situation catch the first SAS ground staff you can find and alert them to your situation. They will always call your gate and inform them that you are on your way. If immigration is involved, cut the queue and ask the officer to clear you as you have a connection in 10 mins.

Regards Oliver