You don't have to deal with this by worrying (or by avoidance so you don't have to worry). That doesn't do anything, anyway, save create stress. The way to deal with it is just by doing what you're doing: getting all the information you can, then thinking about it, then talking about it together with your partner.
Per the stats you're asking for, let me poke around a little bit more and circle back. That information is obviously going to be tricky to come by, because a) acquiring the virus when the carrier is asymptomatic is far less common than the alternative, and b) it's very hard to study something that isn't happening and that people don't usually know about. I'm not finding anything new or that specific on it in a cursory swoop. Based on what I know, I'd say it's rare, but I haven't tried to find this particular info in a while, so I want to make sure I'm not missing anything new. I'll hop back after I do that a little more, I just didn't want to leave you hanging.
I'm also happy to talk with you about how to make dam use feel better if you're interested, now or later.
I do think that whatever choice you make with this, it would probably be beneficial to rethink some of the ideas you have about this stuff, because not only do I think they're probably playing a part in your decisions (and not in a good way), you may well have to do things like add safeties for yourself or other partners throughout life. So, I just want to take a sec to quickly debunk a couple things.
Intimacy is emotional, not physical. In other words, the intimacy we experience with physical sex is something we do because of our brains and our emotions. Even our idea certain things are more or less intimate is itself intellectual. A condom or a dam can't get in the way of intimacy (unless risk-taking is something intimate for you), just like a prosthetic hand, a sex toy, a piercing, an inability to get an erection, or a lack of desire to have intercourse can't. Heck, people don't even feel barriers most of the time once they know how to use them and get good at it. So, one, be it now or later, if and when something is involved in sexual intimacy besides just your bodies with literally nothing else, please just know nothing like that or a million other things are impediments to intimacy, and sex without any of those things isn't more intimate by default. <3
I want to make clear that an STI, herpes included, isn't harrowing circumstances. Herpes is one of the most common infections on the planet, and particularly if you're with someone with it, it'd be good for everyone if you can dial that down some and normalize it, you know? Getting an STI also is something that happens to people all the time, including to people who are each other's first partners for all or some kinds of sex. Not getting an STI isn't a reward for good behaviour, just like getting one isn't a punishment for bad behaviour. The hardest part of living with any STI (or infection like oral Herpes that can be classified as such and transmitted that way), assuming a person doesn't become very ill, is usually social stigma. That can be a lot harder when it's in your immediate life, and sometimes even partner who have internalized stigma and aren't being overt about it can wind up having it leak out in some ways.
So, for your partner's sake, but also just to give you something else to let go of that can mess with our heads when we're trying to make these choices, I'd encourage you to just take an inventory of how you think about things like Herpes and see if you can't start to adjust that a little so instead of thinking of it as a horror, for instance, you think of it like you might think about a flu, arthritis or even COVID: as value-neutral. Get what I mean?
Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it is the only thing that ever has. - Margaret Mead