How to have BF dynamic + discretion?

Hey community,

about a year ago, I gave my wife the permission to have adventures with other men. She had a few encounters but nothing ever materialized. Of all the potentials, the first one started acting like a jerk on the lead-up to their first encounter and a few afterwards got cold feet.

A few months ago, she met the perfect guy. He just hit on her on the streets and they exchanged numbers. My wife directly told him that she is married but can play with others. He was fine with that and then it was a lot of texting between them.

On their first few dates, they met in a pretty secluded place and they did a lot of talking and kissing. This went on for a few dates at the same place until they went into a shopping center together where my wife let him play with her boobs in the changing room (which he absolutely loved). However, in all these months, he seems to be fine with just that and he never initiated more than kissing/fondling. He is obviously totally crazy about my wife, who is very gorgeous. If I was him, I would have gotten a hotel room on the first date (and my wife would have gone with him, for sure).

I am pretty sure that he has feelings for my wife. Also, my wife really enjoys the dating aspect, as I was her first and she can experience things she "missed" without dating other men before. We obviously talked about it and she wants a real connection and feelings, not just sex. She's really gotten such a glow-up out of it, is much more confident, and our sex is the best we've ever had. The whole experience has strengthened our bond so much more.

For me, I would feel very comfortable with them having a boyfriend + girlfriend type of relationship. I know that many people here would see it as a red flag. However, knowing my wife, I am certain that she would end things if it would endanger our marriage - even if it hurt them.

In all of that, I basically gave my wife two rules: Safety is always priority #1 + she must be discreet as I don't want other people to know this. For reference, we live in a <1M urban city.

This leads me to my actual question: Is there any way for them to have a boyfriend + girlfriend dynamic while being discreet? I would love to just tell her: Go to a nice restaurant or bar together and let loose. However, I also don't want to have to explain our arrangement to friends and co-workers that might run into them.

Anyone that has experienced something similar?