I would avoid adding any water or liquid. It seems to make the litter clump and get gummy more. I am not sure why now your kittens are getting it stuck in their paws....and not before. Just make sure to keep the litter box clean as possible so they are not stepping in the wet and having the litter stick to their paws. you might also want to put a small rug of indoor/outdoor carpeting as the kittens step out of the cat box...it will help to "splay: the toes and remove excess litter.
When I got my cat neutered the vet told me to put shredded paper or newspaper in the litter box instead of litter until he healed.
Maybe you could try that until your kittens heal to avoid getting any infection from dirty litter stuck in their paws.
I'd guess take a rag soaked with water and I dilution of hydrogen peroxide. Dab at it carefully. Use a tweezers to get any bits out that won't come out. Soaking the paw in the same mix can work, if kitty will allow it.