Good morning secretposter. What's your biggest fear in coming clean to your wife? Are you worried that she is going to leave you when she finds out that you've been seeing someone else? Are you worried that she is going to forbid you from seeing the other woman? In either case the chances of this happening are much less likely if the truth comes from you, rather than her finding out from another source. Also your wife deserves to make an informed decision for herself about what structure HER relationship takes.
If this really is a deal breaker for her and under no circumstances does she want to be involved in an open relationship then all that is happening is that you are putting off the inevitable. If, though, there is a chance that she will be open to you having other loves in your life then the work has to be done on both your parts eventually and it may as well start now.
There is no easy way out of this and no guarantees. You're not going to know what her reaction will be until you tell her about what has been going on. This isn't going to be easy at all but it does have to be done so you can move into the next phase of your life, whatever that is going to look like.
Everything will be ok in the end. If it's not ok it's not the end.