Hi - I am a WS, and I think I will take a stab at this for you.
First, it doesn't matter if it was just a one night stand. It would be maybe easier to understand or rugsweep, but you need to know your wife has work she needs to do on herself to make herself a safer partner. I would say that those who do that sort of work, and really take accountability for what they did, and is empathetic and remorseful are a better bet.
When a WS has an affair several things are present:
-They felt a false sense of entitlement for some reason to do it (I work harder, I make more money, I don't ever get what I want)
-They have boundary issues with the opposite sex, and probably boundary issues in general
-They don't believe cheating is wrong in all circumstances
-They are able to compartmentalize to such a degree that they were able to not make you a consideration in their decision.
-Often they have complaints about the marriage they also used to fuel that feeling of false entitlement and they need to learn to communicate their needs and feelings as well as let go of resentments.
That's at a minimum. I stopped there because I am familiar with your story. For many others there are way more issues - history of lies, justifying the affair to such a degree that they villianize the BS, gaslighting, other abusive actions and words, and I could really make this list long if I wanted to.
I kept it basic for the idea that I know your wife had a one night stand, confessed immediately, etc. I would probably be in your camp that I wouldn't be willing to throw away a 21 year marriage right out of the gate.
But, your wife needs to go to IC and figure out the deeper issues - the whys, the hows, get really honest about her blind spots and be willing to do anything that you require and beyond.
Phone transparency, removing friendships that would support this type of behavior, considering whether Girls Night outs are still on the table and in what capacity. For the record, I do go out with the girls and have mostly since my affair. But, these are people my husband knows, did not know and would not have supported my affair, and we are talking dinners where I am home usually no later than 10 or 11. I am actually usually in by 9 but occasionally I will go to trivia or there will be some sort of live music. I am not on lockdown, those things are actually things I just did without prompting. I do not feel stifled by them because what it most important to me is that my husband feels secure with my movements, that I do not cause him further stress or alarm or trigger feelings I gave him during my affair.
So, I am giving you these examples to say this:
Yes, the type of person I would gamble on (and I am currently doing this) is the person who can see how much they have hurt you and does everything they can think of to try and make it up. They dedicated to working on themselves so it doesn't happen again - and I am talking long term work, IC, dedication to reading and learning about themselves, and shows nothing but unwavering commitment to you and the marriage above everything else.
And, even some of those people will cheat again.
So, here is the second part of my advice: Quietly and logically develop an exit strategy. Not because you know you will use it but so you have peace of mind of what you will do if you catch them breaking their agreements or God Forbid cheating again. Work to heal yourself and protect yourself. When you do these things, you will find you are no longer committed to one specific outcome, and that you will actually be fine with whatever happens.
That sounds cold and calculating, but it's needed. Don't rugsweep this, if you go that route I think it increases your chances of it happening again and worse.
I want R with my H, and I believe (mostly) that he wants R with me. If he consistently shows me that over a long period of time, I am willing to move forward. If I catch him lying, talking to anyone inappropriately, or get any whiff that he's not in this to win it, then I will divorce him. I don't want to do that, I do want to be with him. I just won't do it at my expense. I wouldn't want him to do it at his either. This is just not something that someone can say Whoops I am sorry and all is good with the world. This takes a lot of time, effort, and change.