[N*Caddy]

I swapped the ignition on few of my parents or relatives cars, none Cadillac though. I do remember (even they were different makers and models) the procedure was pretty much the same: remove all the plastics around in order to get to the screw (screws) holding the thing in place. Once loose turn the key to some position (varies from car to car) and then pull the module out (two of them had a secret – well some how hidden pin that you suppose to push in to release the module while the key in a certain position other wise is locked).
I think I saw a post somewhere here about replacing the ignition and I think the key trick is also required here. But since you say you can turn-it anyway…you should be fine.