Do you have any anti-static bags lying around? If not, see if you can get some from a local computer shop. I would also STRONGLY suggest a grounding strap (properly grounded of course). You can get one pretty cheap at RadioShack. If you have the money, you could also spring for an anti-static grounding mat, but you can get by with just a bag too.
Minimize contact with the CPU as much as possible so make sure you have everything ready to go before you remove it. Handle the CPU by it's sides only.
You will not need to use force to remove the old thermal comound, just a gentle hand, q-tips, high quality rubbing alcohol, and patience.
Place the anti-static bag on a flat, sturdy surface. Place the CPU on top of the anti-static bag, holding on to it by it's side. Dampen (not dripping wet) a q-tip with alcohol, and start to gently brush away the old thermal material. Try to stay away from any exposed contacts on the top of the CPU. Remove ALL of the old material. Use as many clean q-tips as needed (they're cheap so use em).
Wait a few minutes for the alcohol to completely evaporate and follow Arctic Silver's instructions on applying Arctic Silver 5.