You are very kind to think of the good of your wife considering the whole situation. An awful lot of people wouldn’t care how their ex spouse fares.
My own divorce was a happy thing. I was so relieved and looked forward to a normal, stable, life. I felt terrible for the children, but their father was not a good example or influence for them and our home life was not a good environment for kids. My ex was a chronic liar, cheater, extremely immature, physically and emotionally abusive, on and on. He isn’t a bad person in his heart. I think he is literally mentally ill. It took me a long time to stop hating him and to let go of everything he did to me and the kids.
The divorce was final October 2002. I’ve remarried, had another child, bought a home and I was certain that I had come to terms with my first marriage and all that went along with it. I was wrong!
When my husband came back to the Church, I decided to come with him. Of course, that meant applying for annulment. I highly recommend the process. I spent a few days filing out the paperwork and I was astonished at how much baggage I was still carrying around. The annulment process has given me peace and understanding that I would never have had without it. Certainly much more than the civil divorce did.
Even if you never intend to remarry, I think an annulment might be worth considering after the divorce is final for the healing it provides, if nothing else.