I have Herpes 1, could I give Herpes 2 to my boyfriend?

HSV 1 only appears on the face as a cold sore. I know that if you have it, it definately will not turn into HSV 2 on your own body. But with HSV 1 (and if it's not currently activated on your face), if you give oral sex, will it turn into HSV 2 on your partner as gential herpes? Or will it remain HSV 1 but only as a single cold sore on the gential area when activated?