So, basically there is a risk of getting HSV1 on the genitalia from someone with a cold sore on their lip, but it is a pretty slim chance. (??)
Howdy.
They are two different virus types, although they belong to the same virus family. They are what they are and do not turn to anything, whatever the location is. HSV1 is more common in the mouth region since it sheds more often there comparing to a genital HSV1. Another factor may be that kissing is much more common action than oral sex, thus many people already have oral HSV1 and thus are pretty resistant of getting the virus again to their genital region via oral sex.
On the other hand, HSV2 is typically in the genital region, but can - although very seldom - occur orally as well. They are not the same virus, please seek more info about shedding since if may differ a lot depending which virus you have, and where you have it.