"thermal paste remover"
Even a dry, clean cloth will take most of it off. A lot of people just use rubbing alcohol or similar. I use Acetone (paint thinner).
If the stock heat sink still has the original thermal pads on the bottom (which is to say it was never used) then just remove the old stuff and use the cooler. But if it was also already used, you really should just go buy a $10 thermal paste.