what kind of surgery are you having? will you be laid up in the house for a while? if so, you might want to put off fading until after, so that the congregation can take care of you. :) they love to do that sort of stuff, you might get some yummy free meals. :) go to a meeting, and be really concerned about how you're going to cook and clean while you're healing. they will run to your aide! (if they are a good congregation they will). my old cong. would set up meal rotation schedules.
and AFTER that, fade slowly, but don't take too long to fade. What I'm finding, is that the more confident i become in my choice to leave this destructive organization, the more irritated i become when i try to hide and lie to them. i feel like it's letting them control my emotions, and that is exactly what i'm trying to escape. so fade at first, but build up your courage too. collect, in writing , all the solid facts that led you to your decision, so when it gets to the point where you might have to explain your stand to close friends and family, you can say, "you are welcome to read over what i have discovered to be true, but I'm not going to argue scripture with you".
but that's a ways away. my advice, after all that: don't put yourself in a bad situation before surgery, then fade slowly taking the advice of everyone here, but rememer to stay confident in your decision.
best of luck!
SB