"The baby has a soft, smooth skin" means that someone else may have rough skin, but the skin of the baby is soft and smooth. It would call attention to the difference between the baby's skin and someone else's skin.
"The baby has soft, smooth skin" means that the baby has skin that is soft and smooth. It does not bring anyone else into the equation. This sentence is just a sentence about the baby, and does not compare the baby to anyone else. If you are just looking at a cute baby, this would be the right sentence to say.