The difference is history and circumstances. For the Kate AU, you have to keep in mind Cy never met Lynn in college, didn't become as socially developed, and key point here, never was introduced to kink. Even if Cy has a pretty strong libido across most universes, the reason he starts cheating on Lynn is because they were doing chastity kink play and he got frustrated at the fact denying her meant denying himself too, in a way. This version of Cy isn't kinky, doesn't see cheating as a "game" between Kate and him, so when she asks him to quit sleeping around if he wants to go steady with her, it's not a very big demand— they're not in a D/s relationship! As for the Divorce AU, it's less that Lynn threatened to leave, and more that she just up and decided to leave one day because Cy wasn't taking her emotional needs seriously, the cheating was just one part of it.

He'd probably be weirded out by how joyful and expressive canon Cy is, and he'd probably be a little envious, but also very glad he ended up with his Kate.

I think it's the kind of thing he'd have a weird horny dream about once and then dismiss.

Oh yeah, one of her conditions for going steady in that AU is them being exclusive. Cy relents.

It could happen too, and if Kate ever found out she'd find some way to justify it ("it was a long time ago, he's changed since then").