Mik, you need to have a VERY SERIOUS sit down with your wife and ask her if she is going to refuse sex to you from here on out. And if she answers in the affirmative, than you ask her "Do you expect me to live out the rest of my life without sex?". What this does is indirectly show her that the life that she is attempting to doom you to, is selfish, not realistic and a deal breaker. It forces her to see that it is ridiculous for her to expect you to live your life as a priest.
If she is responsive to your frustration, then you two can work together to compromise and figure what you both need and require to help the other be sexually interested; whether it be more intimacy, counseling, weight loss (ie. making oneself more physically attractive), medication aids, etc. However, if she flat out refuses, and will not work with you, then you need to make the decision to either A)live the remainder of your life as a priest, or B) begin preparations for a divorce, so that you can go about finding a spouse that WILL fulfill your needs.
Cheating on your wife, is way, WAY worse of an act, than she is doing to you by denying you sex. Why even be married to her then? Because all of that talk of being "happily married for many years (and by 'happily' I mean we still laugh with each other, spend time together, try to make life easier for each other, etc)" is then, all a lie. Would you be ok with her having an affair behind your back? Probably not, which would make you an enormous hypocrite.
And then there is the practical problems, like contracting an STD or possibly knocking up an affair partner. Either way, affairs also have a very ugly habit of surfacing in ways that you never expect and you will probably get caught.
Talk to her and rationalize with her. If all else fails, divorce her, before you go banging any strange. That is what a real man would do.