Re: I am the cheater
I have unfortunately been in your wife's shoes & know where she is coming from. I do think it's good that you are putting thought into how to approach the subject, because the hurt is very raw and real but the longer you hold off speaking to her will risk that any healing she has done will take another blow and at some point will be one too many for her heart to handle.
What she probably needs to hear is:
The issues from your standpoint that made you feel the need to seek someone outside of your marriage...was it sex? lack of attention? lack of appreciation?
Of course, this should be approached delicately and should be prefaced by 'I want to tell you how I was feeling at the time because I'm sorting out for myself why and how this happened, but so you know in advance what I was feeling then was no excuse for what I did. I take full responsibility for that & in no way am trying to push blame.'
Acknowledging that you can put your finger on the state of your marriage at the time will give her a sense that there are things you both can do and will give her a better sense that it will not happen again. Saying 'I don't know' will just make her think if he didn't know then, he won't know the next time he's in that situation. Give her some assurance that the things that were lacking are things you not only intend to work on but that you will communicate with her clearly if you are feeling distanced again at some point.
'I don't know...it was innocent at first...she was just a friend...then, it was like a freight train...once it started I knew it was wrong but didn't know how to stop it'...this might be what you felt, and if it was, you need to think about your boundaries with women going forward and communicate them to your wife. She will appreciate that you are doing something to prevent this from happening again. Maybe for you, the boundaries are that you do not have any personal discussions with women, you do not go to lunch alone with a woman, etc. but in general, a good rule of thumb is to tell her that you will think of her standing right next to you anytime you speak to another woman to ensure your conversations are not inappropriate.
It is very difficult to picture your spouse having an emotional connection with another woman, especially if they know you are married. You have to assume they did not speak kindly of you or the marriage. The feeling of betrayal is unreal and you feel your vows have been negated and that your feelings were not considered by the one person who should consider them the most. The physical images are no better.
How long ago did this happen? Do you still work with the woman? (that will make healing/rebuilding trust much harder for your wife)
If not too much time has passed, my opinion is it would be better to come fully clean with her...I'm sure it's hard to do that when you are initially confronted off-guard and if it took you an additional 4 weeks to break things off, I'm guessing you didn't want to come clean for selfish reasons. If she knows you are speaking from your heart because you want to be totally honest with her she will feel more secure within your marriage. There is always a risk in disclosure, that it will just be too much, but she wants all of you at this point...keeping these secrets will prevent you from giving her that.
You have an opportunity to have a stronger marriage than ever before, but it starts with respecting your wife and wanting to have your closest relationship to be with her.