Certainly if removing the stock heatsink, a dry cloth or even paper towel is fine. What you'll find on the processor is dry and comes right off. Just keep wiping the surface until the top of the chip is totally clean. No need to remove the processor. The new HSF may require you remove the entire motherboard unless your case has an opening under the processor socket to attach the backer plate.
I see, thank you
I've got a Fractal R4 so no worries about removing the motherboard fortunately