Cold sores are actually quite dangerous for young babies. I don't wish to scare you, I'm just advising so that you are fully aware of the risks.
The year my son was born, a newborn died from a cold sore, and I was consequently petrified of them.
Note that these are newborns, and it is rare for newborns to contract it. It is not as serious for older babies, and most children carry virus in its dormant stage by the age of 2, with no issues.