Actually, if you are careful it will remove the colour* from your hands and not your skin if you are quick enough and wash the hands well with water afterwards until they don't feel soapy. It's my weapon of choice when I get ink on my hands after re-inking, but I don't leave it on more than 10 seconds.
Worth going to your local supermarket / hardware store or even checking out eBay for a supply of disposable gloves. Just don't buy the natural latex ones if you are allergic to natural latex rubber.
* The bleach will remove the colour from the ink, but not the ink from your hands. The caustic soda in the bleach will turn the natural oils in your skin to soap, hence you need to wash until you don't feel soapy. Natural rubber latex allergies are a growing problem, if anyone at home suffers from it, don't buy the latex gloves, or at least not the powdered ones. And yes, I do know what I'm talking about, it's my day job :/
Most effective product I ever have experienced: sodium benzoate solution (10 %) or sodium benzoate granules used as soap. Wet your hands and rub a pinch of sodium benzoate granules until completely dissolved. Rub until the colour disappears from your fingers like magic.
Sodium benzoate is not caustic or is very oxidative like bleach and is completely harmless. Actually you can drink the solution to some extent without any harmful effects. It is used as a preservative in sauces and used as expectorant in cough syrups.
One thing: this trick works only with dye inks, not with pigment inks.
I think the mechanical debriding action is the most important part. You don't need to rub the skin raw either. I think the ink resides in the top layer or two of the skin (seven layers total) if gotten too soon enough, like soon after finishing the refill. Not all the ink may be removed initially, but the majority will be gone.
It is a cheaper workaround and without potentially caustic chemicals.
My boss once noticed my hands had black stains on them and asked if I was working on my car. He likes to work on cars and thinks that's cool. When I told him No, I was refilling ink cartridges, he was disappointed. So just tell everyone your car needed work. (It does, doesn't it?)