I'm usually a follow-through person when it comes to what I've said standing, but that's one of the reasons I never offer to take away a party or rare/special event or holiday celebration. In my mind you're not only punishing your son, but the child who invited him to the party. It's also unfair to the birthday boy's parents who have planned for a certain number of kids and perhaps had to pre-pay at the bowling alley. They may have told their son he could choose 5 friends, and if your child suddenly doesn't go -then he could have chosen someone else.
It also sounds like this isn't working anyway since he hasn't stopped misbehaving. I would make it more concrete -along the lines taking away a favorite toy or no tv for a week or some chore he hates (raking leaves or something). You should present this to him as telling him what the punishment is going to be for his week of misbehavior, but tell him you don't want to also punish his friend and that it's also important when you say you'll be at a party or event, you should go unless you get sick (given the absolute horrifying rudeness of people RSVP'ing these days -it's an important point to instill).
Is this week's misbehavior out of the blue? Has this been going on a long time? If this is all of the sudden -have you tried to find out why he's all the sudden acting this way? Maybe you should speak to his teacher. What does she consider bad behavior? Has she given you specific examples? Is he breaking class rules, talking back and being disruptive or has he just been fidgety or zoned out and not paying attention? I have to express concern at him being at a school where they still use corporal punishment. I'm not anti-spanking, but if someone else ever laid hands on my child I would come close to killing them! I believe a few pops on the butt with a hand is one thing, but you have no idea how hard this headmaster may hit your son! What is he going to hit him with? How old is your son? By the time kids are in school, spanking -especially a public one in school - serves no real purpose except complete humiliation and a furthering of your child's hatred of school. I used to teach and I went to school when kids got paddled for everything, but the kids who always got paddled never stopped acting badly!
I wouldn't take the party away and I would search a little deeper into this situation at school and talk to my son about his behavior. It sounds as though you need a different discipline strategy all the way around since the ones at school and at home aren't working.
****OMG **** I just read your update! He's eight, gets stressed out over timed tests and has ADHD and you THINK IT'S OKAY THAT HE'S GETTING SPANKED AT SCHOOL?!?!?! WAKE UP -THAT'S DISGUSTING! Yes I'm yelling because if you were standing in front of me I certainly would be! Do you have any idea the amount of anxiety, anger, stress and general upset you're instilling in your son by sending him to this place? No wonder he can't behave there! This is only going to get worse. You should have him seeing a counselor until you all find the way that works for him and what kind of learning environment he could thrive in. Obviously you have the means for this since he's going to private school. You need to find another school immediately. If this school can only control its students by hitting them with paint stirrers, it's a pretty sorry excuse of a place -especially when they have diagnosed learning and behavioral issues! Geeeez -that makes me sick!