Welcome to our Forum. There are no specific studies of how commonly transmission of HSV-1 through casual contact is. The rates are low. Equally importantly however, I feel I need to point out that there is a certain (unknowable) risk that your son may acquire HSV from you (or someone else) through casual contact. I hope that possibility however will not keep you from regular contact with him (i.e. kissing, hugging). HSV-1 is just not that big a problem (over 60% of adults have it) and to not be close to your son would be a large price to pay.
I hope this comment will help. EWH
I should also add that my toddler has eczema, which I know can make hsv1 worse.