Is there an inexpensive solvent I can use to dissolve thermal paste without scrubbing?
First the sad part - there is no magic compound that will dissolve thermal paste like a champ and leave your electronics alone. If that was no "sine non qua" as they say, we could have suggested a varied assortement of highly aggressive halogenated solvents which we would mix with something else for the extra bang, some hydrogen peroxide perhaps, or the good old fuming nitric acid. Things would happen, rapidly.

As for all-round no-nonsense solvents, isopropyl alcohol is a big favourite, it is fairly environmentally friendly especially if you consider your hands and your tabletop as part of the environment. And of course it solvates a wide range of icky substances that needs removal. As a small step up the agressive solvent ladder would be to consider acetone, "citrus solvent" (basically oils and acid of lemons, it kicks ass) or acetic acid based solvents. But none of them will magically clean the surface, you'll have to use some elbow grease. Or thumb grease, I guess.