What testing did you have done? If it was a blood test, posting your results here can help us see if you had the right testing done and if you need additional testing done or not to confirm your status. Since you've never had symptoms, well worth posting results here.
Make sure that your partner had herpes igg blood testing done. It's not a part of routine std testing and he might only think that he had herpes testing done.
Is your partner likely to contract hsv2 from you when you have no symptoms and you are on daily suppressive therapy? No it is not. He should never perform oral on you when he has active cold sores or healing ones.
Contracting oral hsv2 is certainly possible esp when there are genital sores present. I say its possible but its not common at all as hsv2 does prefer the genital area. Do be aware that if he has hsv1 oral you would be more likely to contract that genital esp if he has a lip sore at the time.