Although I'm new, I hope my advice is correct, since it worked for me... 😎
I just used some rubbing alcohol and a couple of Q-tips and cleaned it off the core and around that area, too. Use a couple more to dry it. I waited about 10 minutes for it to dry, since it was alcohol (it evaporates/dries quicker than water). Or, just eyeball it. I think you could tell (I hope you could...)
As for the Arctic Silver, start with one drop. Use a razor, and at an angle, coat the core as thin as you can with a razor. Then use up to 3 more drops until you have a <b>very</b> thin coat.