Not necessarily TTC but more after baby?

So I was just having a panic moment about this last night for some reason. My boyfriend gets cold sores which I know is HVS1 but I’ve always heard that it could potentially pass from his lip to my girl parts if I allowed that to happen cause HVS2. When he has them however I don’t kiss him or anything because I’ve never had a cold sore. But my question is, when we have a baby, would he be able to kiss our baby if he didn’t have a flare up? He only has the cold sores not gential herpes. But then I was also wondering if I could possibly just be a carrier and not actually get flare ups or anything, if that was the case would my baby be born with HVS1 virus? I’m not even pregnant we’re TTC but this became a huge thing in my brain because I’ve seen so many babies get sick from people kissing them with cold sores. So I wasn’t sure how it all translated I guess. Any info would be so helpful in easing my mind.