I made a promise to my wife after I told her about my affair, but I don't think I can keep it.
Really? Why can't you keep your promise to your wife?
I promised to never lie to her again, but the truth will hurt her deeply.
Breaking promises is one of the easiest ways to destroy the trust and credibility you've worked so hard to build. It not only disappoints the person we've promised, but it also erodes bits of our self-esteem.
The truth will be too painful for her and it will end your marriage.
This issues between you and your wife sound very deep. You should keep the promise and not lie to her. If the truth is painful, the two of you should consider counseling to work out your issues and try to save your marriage.