This isn't rocket science people, and unless you are gaming and likely overclocking bringing the cpu to it's limits I wouldnt worry about it too much. What I would worry about is if it were a laptop and the exhaust vents were plugged and the paste were old and dry thus not disapating heat at all as well as the exhaust issue, you are heading towards disaster with the cpu & onboard GPU overheating, so basically just get it on there, Arctic Sliver is the best and dont get it on any components to cause a short and have your laptop cleaned once in a while. I take the fan right apart and clean it good with a toothbrush and alcohol. Some fan blades will gently come right out of it's socket. Just dont clean the grease off of the shaft - clean all the fins and the fan blade itself gently and dont lose the small washer off the inside of fan shaft but do get the hairs out of there.
Dont force the fan out, some are not removeable.