K.K.
Stay at home and have your baby and your baby will never leave your side :)
I have 3 children. One hospital birth, and two homebirths. I am also a midwife and a former NICU Respiratory Therapist. Your baby is your baby. You tell the hospital staff what you are going to do. If you don't won't your baby to leave then tell them the baby will not leave and whatever they need to do they can do in your room. If you want to give your baby a bath tell the staff you will take care of it. It is not even neccessary to give the baby a bath until you get home. The vernix on the baby is very good for their skin and should not be washed off.
Don't worry how anything will go over with the staff. Remember you are paying them for a service. You are the one in charge. Tell them how it will be. Also don't worry about what any "policy" says. Policies are not laws. They do not have to be followed by anyone that does not want to follow them. If any staff member tells you that there policy is such and such tell them you don't care. You as the parent will decide what your baby will do and won't do.
Blessings to you.