Awww, Sadie will be just fine.
She may be mad at you for the "birthday present" but she'll forgive you. lol. You'll just have to love on her extra and spoil her rotten when she's all better, and have a birthday party with lots of treats and presents.
Talk about feeling guilty, Hot Rod had 14 teeth take out at his neuter! He did fine and so will Sadie.
Let us know how she does.