What you describe is typical of an unregulated power supply.
A regulated 12v supply should always put out a steady voltage very close to 12v, until the load becomes larger than the supply can handle. At that point, voltage will start to drop, probably pretty quickly.
OTOH an unregulated supply will behave as you described. With no load the output voltage will be higher than the nominal voltage. With heavier and heavier loads, the voltage will go lower and lower.
An unregulated supply killed my previous CC. The label said 14v. And the CC should work with voltage up to about 14.5v (based on what I've read several places). The previous owner assumed it was OK; I bought it on eBay and did not check the voltage when I received it. The CC worked for a few days, then smoke came out and it was dead. After that happened, I checked the supply and found that with no load it put out 20v! (definitely unregulated) That was much more than the CC could handle, and eventually something failed on the motherboard.
Having said all that, I have never seen a supply that behaves like the one I'm asking about. Even with no load (actually the meter is a very small load, several thousand ohms), the supply output voltage "pulsates" if you can picture that. Connect the meter, and it reads ~12.2v. Then as you watch the meter, the pointer slowly drops down to ~11.5v. At that point the pointer jumps quickly up to ~12.2v. Then it starts slowly dropping again. If I had to guess, I would say it's a regulated supply (after all, the voltage swing is relatively small) but there is something odd about the time constant of the regulator circuitry ... maybe an open output capacitor.
So the key question: is this normal for an original CC power supply? (It has the Chumby name stamped on it.) Or is it malfunctioning, and thus liable to damage the CC if I use it?
I guess I need to get an appropriate sized load resistor, and look at it on a scope, to see if there's a lot of ripple. I was just hoping Duane (or someone else) could tell me offhand whether this behavior is typical and safe.