Cold sores and future partner?

So, as in my school and all I wasn't "deeply" educated regarding STDs, I never thought about the cold sores of my mouth as such, until a bit ago. I barely had contact with one partner in my life and unless that person hid it from me, I never passed it to them.

But now that I realised that is such a contagious disease (even when there isn't a visible outbreak) and can actually damage people in their genitals (if they got it from example from me performing oral sex), I've begun to worry.

Not that much about me, but about any future -possible- partner.

I've started to think that, if I got any chance to get that kind of contact, I should tell them, as it seems like an actual risk.

But it also feels like such a "deal-breaker" or, at least, really humiliating. Like, can I expect anyone EVER to take the risk if they know about it?

And yet, I've seen that the cold sores are a "fairly" common disease.

So I guess my question(s) would be if I am overblowing it, if I did miss something, or whether I just should be straight-forward about it to anyone that in the future would want to approach me that way. Anything about it would help me, maybe what you thought when (if) your partner told you this, as I am not sure what to think about it, thanks...