there is still a product out there called "Pretty Feet and Hands" which is a mildly ionic solution that loosens dead skin (start with it freshly washed and dry)... it will take a few minutes, and then loose dead skin will slough off with mild rubbing with a damp cloth.
wash with soap and water and apply skin cream or lotion afterwards.
Soak your hand in hot, soapy water and use a pumus stone to scrub with. Coco butter, aloe, or broke vitimin E tabs rubbed into the skin of your hands will solve the problem.
soak your hands for about 10 mins.
then wash and repeat if you need too.
Might be worth trying to moisturiser/ hand cream/ cocobutter.
Put it on before bed...and when you wake up.
Use a pummice stone after you've soaked your hands for a while.