Well, good on you for coming here and posting, at least. Since you know the sort of reaction you're going to get, I see that as a desire to change.
No secret in life is completely safe. Do you really think your wife might not find out?
If/when your wife does find out on her own, what do you think her reaction will be? Worse or better than if you told her yourself? Do you think you'd ever be able to fully gain back the trust you'd lose? How much of the progress you've made in therapy would be blown out of the water by her finding out?
That doesn't even touch the questions of what happens if you get an std, what happens if the other woman gets pregnant... these things do happen.
You can either passively wait for this to explode in your face or you can deal with it proactively and hopefully have a lesser explosion on your hands. Which would you prefer?
My advice is to tell the other woman that you plan to tell your wife and that you need a little time to work things out at home, you don't know how much. Then cut things off. THEN tell the wife and explain the step that you took. Tell her that you know this must be very hard to accept and that you're so sorry but that you love this woman amd you want to try to find a way to move forward. No one can guarantee her response, but others have made this sort of thing work. A show of good faith can only help your chances, plus give you back a little of your self-respect.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.