Some of the responders will answer under "woman", but have a penis, and I'd prefer to be clear that the division I'm making here is one where genitalia is important
Vagina is a biological physical descriptor though. It seems you've made a weird and unnecessary concession to activists. My answer would be that with a woman I'd like it, but now that you've put that in doubt I can't answer.
It's weird to assume that people would consider a woman to be someone potentially having a penis. Do you really think you'd be using 'vagina'd person' if a lot of mainstream organisations hadn't used similar obfuscation of language over the past year?
No, I wouldn't, but that's sort of besides the point. If I used the terms man and woman, then a lot of people who have penises, would have selected 'woman', and since I assume that this category of ppl are meaningfully different from cis women, it would have skewed my results.