This is tough. I am a closet drinker too, but I overcame it by choice. Alcohol just makes me sick now, and its not really worth how it makes you feel in the short term rather than long term. The lying is very difficult to deal with and that's what makes it all the more painful. I have never dealt with an alcoholic myself, but I did deal with a drug addict.
You're 60, you still have some good years left, and they shouldn't be miserable. Life is very short and we have to enjoy as much as we can of our time here on Earth.
Seeking therapy is a great step, and I hope your wife comes around and decides to help herself. Good luck to you