He sounds like a best friend of yours, while honesty isn't always the best policy with this specific situation it comes down to what you really feel in yourself on what you should tell him.
Personally me, I would just tell him the truth. If I've known them for 41 years and we're best friends like that. It would be difficult for me to do however, because I understand that you don't want to mess up being his drinking companion, but that's out of ones control. And to me, it would be better than playing it off. I always feel better when I'm honest. Then I would feel like I'm giving him a sincere reason why vs some made up reason, to some one I really care about. It would make me feel good because I am being open and honest with some one who means a lot to me.
I would say some thing like--
"Uncle, I wanted to tell you some thing, I really want to have a drink with you, but I can't anymore because I quit drinking"
But that's just me, it's up to you on how you feel you should handle the situation.
And if you're thinking that you're not putting him first and are being selfish, you're already being selfless by quitting the drink. Because over all too much alcohol is a selfish decision.