Alcohol won't hurt anything. I suggest lapping the heatsink. Mine always has a mirror image of the processor etched to it when I remove it. That means particles of old compound are firmly crushed into the heatsink. I also notice some corrosion which means pits with metal oxides. It all comes of in a few minutes with my homemade lapping array.
The processor does not get lapped. It does require thorough cleaning to remove all traces of last used thermal compound.
Cotton swabs can leave lint. I have heard that coffee filters are lintfree. They certainly are abrasive enough to clean the processor surface. I am using a box of lintless wipes liberated from an Army repair depot decades ago, don't tell anyone.