What is your current cooler? Or is it something that comes included in the case?
The NH-D15 is one of the best coolers out there, in most situations you will see an improvement (improvement in temps/speeds/loudness of the PC or multiple of those).
Is your case the CM H100? That supports coolers up to 83mm, while the NH-D15 is like 160mm or something.
don't need to remove the CPU from the socket
Unplug all cables > remove pump/block combo from CPU > remove radiator seems like the most logical steps