I have had cold sores all my life I get like 2 year. It’s really no biggy. I also have to kids and neither of them have them.
As far as I'm aware then someone's gotta have an active cold sore for this to be infectious. If they didn't have a cold sore outbreak that day, then hopefully the baby's safe.
There's not much you can do unfortunately. Some people have a natural resistance to cold sores so your little one may too if both you and your partner don't have them. The best thing you can do with a cold sore though is catch them and treat them really early so perhaps by some Zovirax cream just incase he shows signs?