If the IgG was high, they don’t need the blot.
If they don’t know if their infection is oral or genital, hard to know what to avoid. But HSV 1 can be transmitted without symptoms, like HSV 2.
We don’t have research on the reduction of viral shedding for HSV 1 (oral and genital would be quite different) but biologically, I don’t see a problem with this person taking antivirals to reduce the risk of infecting you, if they would be willing to do that.
Terri