I flew HKG-AMS-OSL, first leg CX and second on SK in early September 2011. All in C.

Checking bags through to CPH is no problem. Your BP for AMS-CPH you must get from the SK transit-counters. When I transitted, there was no cooperation across Star Alliance, so you really must go to the SK counter to get it.

To get there, you must pass through the Schengen border-control. I faced massive lines when I went through. This was followed by security, with equally impressive lines. At that time there was no fast-track for C-passengers. As other posters report, this seems to be in place now - but since you will likely not yet have your onward BP I'm not sure how you would access the fast-track. Maybe you can get something onboard CX or use the CX BP.

While the transit and all sucks, there are not many airports around where you can bring back DIY-flowers for the wife! Tulip bulbs are on sale everywhere, and went down a treat when I got back home.