Normal Cats and Wolves automatically stand while in water so that they can swim to the surface, but Zombie and Skeleton pets do not swim, so they should be able to be sat while in water.

Zombie and Skeleton pets stay sitting if pushed into water while sitting. They just can't be sat while already in water. I have also noticed that if a Zombie or Skeleton pet is sitting in water and the chunks are unloaded and loaded again, the pet stands up but not visually. The pet is able to move but visually stays sitting.