There would be no risk to transmitting HSV-1 when performing oral sex on your partner if it is just on your genitals.
When HSV enters the body, it will go into the nerves of that area, this means when it reactivates as either an outbreak or shedding it will just be in that area. For example, to pass HSV-1 in the genitals to another person they would need to have contact with your genitals.
As some additional information it is also difficult to know the chance of passing HSV-1 when it is on the genitals and someone is having genital sex with another person. You will find lots of studies that give an idea of the chance someone has of passing HSV when having genital sex but almost all this research has been done with HSV-2 being on the genitals. HSV-1 evolved to be around the mouth area and we find when HSV-1 is around the genital area that it does not outbreak or shed as much as HSV-2 on the genitals or HSV-1 on the mouth.
Let us know if you have any more questions or concerns.