While you can go through the procedure on your own, like Ric, I agree with most everyone on here. Your wife needs to know what you're about to go through. It sounds like you're already doing the ground work on that, so keep it up! You will need her support, and as someone else has already pointed out, you will need someone to drive you to and from surgery. Plus, even if she doesn't understand at first and "judges" you for your decision, AT LEAST try to bring her to one of your meetings with your doc. Who knows, she might "get" it after hearing it from a doc? This journey is for the sake of your health, I'm sure she'll end up giving you her full support. Usually, when people are "against" things, it's due to ignorance -- they don't fully understand what it is, so their default response is to reject it. This applies to many things. That's how I see it anyway.
As for the "keeping it a secret" part. Just tell your wife straight up that you don't like it when she tells her family about your business. Explain to her why you need her, even just this once, to keep this between the two of you. Stress can take a toll on your emotional health, and you certainly don't need that while going through this journey.
I wish you luck on your future surgery.. And I hope you find a way to get your wife on board.