My partner and I have oral HSV 1. What is the probability one could get genital HSV 1 if we refrain from oral contact during an outbreak?

Should not happen. Once you have one type of herpes, you can't get that same type again.
Minimal risk. Your risk should be minimal as you and your partner will have a protective antibody to HSV 1. You will be protected from additional infection by virtue of the antibodies you already have.
Very slim. Usually oral hsvi is not shed if not having an outbreak so do not worry if you refrain form oral contact until the lesions are completely healed.