Like Shiro said, you've got the support of your fellow furs.
And yes, for a surgery like that, you'll most definitely be under some kind of anesthetic, so you won't feel a thing.
The most important thing is to follow what you truly feel is right. If you know that it's what you want for yourself, then nobody can stop you. If people are put off by you, then it's really their problem, not yours. Just brush them off and concentrate on the people who will love you for who you are.
I definitely understand what it's like to be worried about what others with think. But it's not their body, it's yours. And you can do with it what you wish. And afterwards, I'm sure you'll feel great.
It may be jarring at first, but once you get used to it, I have no doubts that you'll be much more comfortable and confident with yourself.
Remember, we're all here for you. If you ever need to talk, you've got an entire fandom full of friends that will do our best to help you through any struggle you may face.