LOL! An antivirus shield! I need to get one of those.
This will probably be the hardest part, if your doctors are like the ones I've worked with. I'd get my charge nurse and the ID nurse to enforce this- post signs on every area you can, over sinks, before entrances, etc. to wash hands and clean stethoscopes before using them. have gloves handy, and if they're going to be coming to your baby, be waiting with a pair or gloves and an alchohol pad.
"Doctor, here is a pair of gloves for you."
or
"Doctor, here is an alchohol pad to clean your stethoscope."
Don't ask them, "WILL YOU clean your steth...?", but say it politely and with a smile. When I have a particularly hardheaded doctor, I have actually offered to clean it for them. I have never had anyone turn me down, but usually they will clean it themselves- sometimes they huff, but I am as adamant as i can be while still remaining polite and friendly. I just say, sweetly, "If you hand me your stethoscope, I'd be happy to clean it while you wash your hands..." and they usually do one of the following: Give it to me to clean, clean it themselves, or use mine (which I clean religiously between patient uses). If they give you a hard time, go to your charge nurse or ID nurse and get some support from them.
We had a problem with this at the last facility I worked at, and actually managed to trace down an infectious strain to a resident who refused to abide by our practices. It was suspicious how only certain babies from a certain medical school were getting infected and ALL of them had come by this resident during his rounds. We cracked down on it and managed to clear it up, but not before our babies got awfully sick. They won't like it necessarily, but hopefully with gentle reminders (respectful reminders!) they'll get the hint and start doing it on their own.