If I remember correctly that link above gives instructions on how to dissassemble the black plastic SECC2 cartridge, and once you do that you may not be able to reassemble the cartridge as it was originally. You will then have to attach the original HS&F to the bare PCB that holds the CPU. If that's what you want to do that's fine. But:
If you only want to remove the fan from the heatsink, then, if my memory is correct (and it may not be), you have to pry a couple of tiny clips that hold the fan to the HS.
Frankly I wouldn't mess with it - you're just asking for trouble. The stock HSF is made to last years and years. They probably use a thermal pad between the CPU and HS which will not dry out like thermal grease.