I think you're making a HUGE mistake if you try to reconcile with your wife without a mutually-agreed-upon (or at least mutually-UNDERSTOOD) transparency plan in place.
The recidivism rates for infidelity are high enough when people put the right things in place: MCing with someone specifically trained in infidelity; strict no-contact agreement; full transparency; etc.
WITHOUT those things? I'd put the recidivism rate way northward of 90%.
You're playing with fire. Giving kerosene and matchsticks to a not-yet-reformed pyromaniac. Your reconciliation can survive your wife's anger over having to do transparency; it can't survive her repeat infidelity. Bite the bullet and endure her anger now, at the front end, and give your marriage the BEST chance to heal and reconcile.