Keurig....
Best paper towels to use are the blue shop towels, they are the most lint free, and hardest to tear when dampened with the isopropyl. Recommend that you use coffee filters for that reason alone, apart from the rediculously low expense.
All you need is damp. If the filter/towel is dripping, it's far to soaked, toss it, start over. In this case, patience is most definitely a requirement, basically for the whole process of replacement, and that includes refitting the cooler. If there's any doubt it's clean enough, keep going. One of the reasons I prefer the gray pastes over the white, if the filter keeps getting discolored, the cpu still isn't clean enough.
When installing aftermarket coolers, get all screws barely started first, before tightening any, the tighten slowly in an X pattern for 4 screw coolers/pumps or side to side evenly for 2 screw coolers. Don't crank 1 screw down, then the other or the paste ends up uneven, the cooler lopsided, or even warping can occur. That'll land you with core temps with large differences.