I've been using the milliput/greystuff combo (playing with ratios) and found that the milliput really gets sticky and nasty on the fingertips when mixing. My first time I didn't wash my hands after mixing, and it dried inside the fingerprint grooves and between the nails, causing me a bit of discomfort. Now I kind of dampen my hands a bit while I mix, and as the milliput kind of dissolves with water (making a white milky slick on the fingers and putty) I periodically wipe my fingertips off on a damp paper towel. Then I wash my hands and I'm in good shape.
I just dip my tools in a little water - does the trick. I did have a paint brush licking issue for a minute, but I cut that out.