Neither of our cats puts its paws in the food bowl, but one of them drinks water by dipping a forepaw completely (above the ankle) into the water bowl, then licking the water off the paw. (The other cat thinks this is absolutely disgusting. ) She also takes turns with her paws–She’ll dip the right paw in, lick it clean and dry, then dip the left paw in, and lick it clean and dry.
The other cat, though, lounges when he drinks water. In fact, he likes to sleep on the bath towel next to the water bowl (which is placed there to absorb whatever cat #1 doesn’t lick off completely), and when he gets thirsty, he just moves his head until it’s positioned to allow him to drink from the bowl. He rarely crouches when he drinks, like most other felines I know. If the water bowl is not positioned correctly, he just reaches out with one paw and pulls it toward him, rather than get up and go to the bowl.