Difficult one. But it’s like the “drunk driver” question, you can’t take the chance that Katie is going to ruin P’s life as well as her own.
So, it’s moral blackmail time. I would have a quiet word with K first, even at the risk of stopping any friendship, and say that you’d heard about the fling and that she hadn’t used condoms….and ask about her sex life with P. And say that he needs to be warned if she hasn’t been tested for STIs on her return, which she may have been.
So, like the drunk driving situation, you need to be prepared to spoil a friendship in the off chance that you will save someone from injury or worse. At least you’ll not lose P as a mate.