I use brake cleaner, just a bit to break down the worst of it. It doesn't seem to affect my skin (though I don't need to use it very much, and always rub my hands with moisturiser afterwards). You can get off-brand cans for a few quid
I don't know what solvent is in brake cleaner but I would check the label before using it as hand cleaner as some solvents are dodgy, eg some fierce shoe cleaning solvent I have included chloro benzene which really can't be good for you
Back when I did my A levels some 45 years ago we rarely used benzene (C6H6 in a ring structure) because it's somewhat carcinogenic, and usually substituted toluene instead. Toluene is basically benzene but with an extra methyl group (CH2) on it. It's very similar chemically but seemingly less carcinogenic. Our then newly qualified teacher said that at uni they'd wash their hands in benzene, but just a few years later it was rather deprecated for use in school, even for us 6th formers.
I do remember using benzene for the "nitrating" experiment as there was some concern that we might end up with tri-nitro-toluene rather than merely nitro-toluene as intended. Can't really see the issue as (a) TNT is exceedingly hard to set off, after all it can be fired out of a canon without detonating, and (b) I don't suppose tri-nitro-benzene is much less of an explosive had we somehow ended up with some of that in the mix