I've always just used kleenex to wipe up paste LOL.
But it wouldn't hurt to give a little tiny rub with some iso and Q-Tips to remove residue then wipe the iso residue away with a kleenex then just let it sit out and air dry for about 30min maybe an hour to make sure there's none left on it.
However, if it's that cheap old stuff that OEM's put in their pre built systems, then it'll be crusty and dried up, and you should definitely use some iso and let it sit out to dry for longer than the 30-60min I mentioned.
Use 91% isopropyl alcohol on some cotton balls. It should dry basically immediately. The CPU would be ready for paste and installation in two minutes tops, because alcohol evaporates quickly. You only need a little to clean paste of a CPU. Wipe it with a dry cotton ball first, then with one with alcohol applied, your done.
I've gotten it at the hardware store. My wife spilled her coffee on her laptop one time, shorted a bunch of the traces. I had to pull the motherboard out and clean off both sides. Works like a champ to this day.
91% is fine.
It softens the paste, making it easy to clear off.
You should be doing a couple passes at cleaning paste off.
The first gets most off.
Do it again to get a very clean pair of surfaces.
I use paper coffee filters which are lint free.
Cotton or tissue can leave lint strands which is not good.
And.. a hint.
Before you try to remove a cooler, run the cpu to heat it up.
That softens the old paste, making it easy to remove the cooler.