Check with your unit before you go ahead and buy anything. Several NICUs will provide stethoscopes for you. At the unit I work at, we have a stock supply of them, and each baby gets one upon their admission. It stays with that baby until they are discharged. Each nurse is able to alcohol the tip off before they use it, as well as clean it off if it falls on the floor. Our aids do a good cleaning after the baby who was using it has gone home.
Our unit invested in all these nice littmans for each baby's bedside but unfortunately more than a few have walked off already. I like the littmans but sometimes the breath sounds are so loud, I can't hear anything else!
I do not even bring my own stethoscope to work as our NICU provides one for each bedside. Plus you would need to clean your's off between listening to each patient every time to prevent transfer of bacteria.
We have dedicated stethoscopes for each of our babies. They're not the best, though. We have some nurses who buy two neonatal Littmanns, one for each baby they're assigned for the shift, and just clean well after each shift.