It depends what the old goop was. If it was a thermal pad (has a putty-like texture), then you will want to scrape most of it off and then gently work the rest off with Q-tips and Acetone (nailpolish remover) and/or Isopropyl alcohol. I think people had better ways to get it off. I used a razor-blade and a very tiny flat head screwdriver. I never touched the core itself, just kinda worked it off by jabbing at it (like getting gum out of your sneakers when you were a kid). For the heatsink, go ahead and make contact, I would use a razorblade just so you don't end up scratching/dinging it with a screwdriver. Get most of it off, and again, work the rest off with a Q-tip and some acetone/alcohol. You can even use water and dishwashing soap with a paper towel on the heat sink. Just make sure it is fully dry before putting it near your computer again. Also clean any soap residue with alcohol. If it is thermal paste (liquidy and white), just use acetone/alcohol with a Q-tip and it should come off. Make sure you have some goop lying around. Personally I prefer AS2 if not for better results, than for the ease of application. It has better texture than thermal grease, making it easier to get a nice even coat on the core.
Chiz