You should look for isopropyl alcohol at the pharmacy or at drug stores, but you can also get it online (500ml for 5$)
You should not use regular ethanol at 96% (the stuff they probably gave at the pharmacy) as this leaves the above mentioned grey haze, which invalidated the purpose of new thermal paste, since the micro gaps will still be full of old thermal paste.
Water is worse than just scrapping, as it adds to the possibility of electrical damage, corrosion; at best it just does nothing.
Some thermal paste brands sell "special" thermal paste remover, but the results don't differ much from isopropyl, these are sold online
I have never tried to use nail polish remover, but I'm guessing real acetone (drug store acetone/propanone) is better than acetone free nail polish remover - be careful with drug store acetone, make sure to read the label. Acetone might not work at all or be harmful like water, as I've said, no experience using it.
I hope to have been of help.