Sorry Big Bill but this is one time where "getting away with it once was OK so it must be OK all the time" doesn't cut it. Solvents of any sort cut through the fatty oils in our skin and penetrate to the fatty deposits in the lower skin during more than extremely momentary exposure. And having it "all over your hands" is hardly momentary exposure. Each time a little more leaches into your system through the skin and for many of them it accumulates in organs where it can't flow past. Over a few years of using such solvents on even a semi consistent basis this will lead to problems. Some are more tolerant than others but either way you're playing Russian Roulette with your body's health for later on. It's just not worth it.
On some folks that are more sensitive to it the results come earlier. A buddy's son got into the auto mechanic trade. The first 5 years of exposure to oils, greases and cleaning solvents of all sorts was a no big deal. Then his system said "that's enough" and over a few months he developed a serious allergy to oil, grease and solvent exposure. Within a few hours following contact the skin would break out in serious eczema (the split, crusty dry skin with bleeding or weeping fissures) that would take around a month to go away even with help from doctor prescribed creams. He tried various barrier creams but nothing really did it. He tried heavier duty nitril gloves but then he didn't have the manual dexterity needed. The thin "doctor's" gloves just tore too easily and he was back to the creams. He finally gave up and went back to school to train for a new career.
Another co worker I knew got the exact same thing right away from trying to use a "playdo" epoxy putty where you massage the two parts together. The skin of both hands was in terrible shape for almost two months. I saw that one happen myself.
A buddy that worked in the autobody trade mentioned that a lot of the old guys didn't live long following retirement and many suffered before going from kidney shutdown or liver issues. The autobody trade is known for liberal use of prep solvents and washing stuff down to clean it and all manner of solvent exposure other than just breathing the fumes. He stuck it out for around 15 years but then got out of it when his doctor saw some problems in his blood tests that indicated trouble.
YMMV but the issues of solvent to skin contact is real.