There actually was a 60 Minutes or some other news show decades ago about a family (I think with a lot of cousin marriage) where many of them due to a genetic condition did not feel pain. And not surprisingly, they had all sorts of broken bones. (I think leprosy also leads to nerve damage that can in part be responsible for the appearance of the affected although I think also there is a direct effect also.)
I would guess such people would be dangerous for a normal kid to play with.
Anyway, pain serves a purpose. I would suggest that when Pris stuck her hands in boiling water to fetch the egg, she was able to turn off pain -- also her skin was more resilient. Leon also plunges his hand into liquid nitrogen, I think.
However, Roy Batty during the fight with Deckard says, That hurt! at one point.
Maybe they can't turn off pain but have both higher pain thresholds, and to go along with this, tougher bodies. This makes sense: no point in experiencing pain if the body is not at risk of damage.