My answer to the question is simply - nothing. You do nothing if you run into the AP. This person is not your friend, and you don't want to change that. Non-acknowledgement is the best attitude you can give, and you're not responsible for the reaction, if any. You just look away and keep going. You owe this person nothing.
I also fantasize about what I would have loved to have done the last time I saw the AP but ultimately just getting away was the right thing to do.
I'll tell my story anyway. The AP was my sister-in-law, my brother's wife, who got close to my husband after my brother suffered a paralyzing stroke and was placed in a nursing home near our family cabin where my husband was staying. I was out of the country a lot, and my husband had just recovered from a long illness that left him without much work. He moved into their house with her to remodel it, and my sister-in-law stayed at the cabin when visiting my brother. (Yes, I know. I feel pretty dumb even writing it.) The two of them became BFFs. They talked many times a day every day when they weren't together but hid their emotional intimacy from my brother and me for three years. When I finally woke up to it and confronted them separately, my husband confessed immediately that they'd had a physical and emotional affair while she gaslighted and played the victim. When I asked her to leave us alone, she tried to contact him through a neighbor and emailed me with touching reminders of our mutual history. WH sent her a no-contact letter, and she announced to me that she would be unavailable - as if it was her idea. The only acknowledgement I ever got from her that she had hurt and wronged me was a small 3x5 card four months later with three sentences: I am sorry. It was mutual. We were needy.
We moved away, and three years later my brother died. SIL organized three memorials for him, and I attended each one. She made three syrupy, disingenuous attempts to hug me. It was not perfect evasion, but I tried my best not to engage with her without calling attention. It was creepy enough, sad, utterly unpleasant and final. I haven't seen her again.
These were awful times and huge tragedies that could only be endured and grieved. Too, too heavy to revisit, so I sometimes sublimate the memory into petty obsession. For example, one thing I couldn't get over was some perfume he bought her. When I came back from my last trip abroad, he started to talk about a particular fragrance that was new and very popular but stopped himself. Later, I discovered he'd given her this fragrance as a birthday gift and gotten himself the male version of it - which I immediately dumped out. I told him how deeply that cut me since he hadn't picked out a fragrance for me for years. I suggested he could still do it and was crushed that he never did.
So I re-enact different versions of a daydream about this stupid bottle of perfume that she left in the bathroom of our family cabin during my brother's memorial. In one version, I dump it out in the toilet and put the bottle back empty or maybe in the trash can. In another, I throw it in the middle of the road, smashing it into millions of tiny pieces. Although the violence of this version is quite satisfying, I invariably redo it so as not to cause any flats. Otherwise, it's the perfect retribution.
But I didn't do it. She would have used it against me if I had. Anyway, I also believe that my complete avoidance is just perfect.
P.S. Do you know that, with my brother's death, this woman inherited our family cabin and then SOLD it to my children? She screwed my husband, inherited the family legacy and made a profit off of my children, which she put in a trust for her children. Such people don't change, and there's nothing you can do or say to them that they will understand.
[This message edited by merrmeade at 7:42 AM, Monday, September 30th]