Get the baby accustomed to the sound of a real camera at an early age. You know, imprinting!
She is your child. You should be able to photograph her in any reasonable way you want. The sound of a camera is not unreasonable. I don't think it would be any louder than the sounds of the hospital clatter that already exist, even in a quiet ward. It probably just seems louder with all the hush-hush.
Flash would be right out. Bad idea and just plain rude. However... If you make a bit of a fuss about the fact that you are NOT going to use flash by the time anybody notices a half dozen shutter clicks the whole affair will be over.
I think the main thing that will or won't cause problems is your manners and demeanor while you are doing the deed rather than the camera you use and what kind of sound it makes.