I don't think so. What does your parenting plan stipulate? Mine says that things out of the ordinary, like extracurricular activities, are split between both parents. This would fall in the "unusual" category, therefore, in which it'd be split. I think it seems pretty reasonable to ask him to split this, it's not like you're asking for extra money every month, or for something frivolous like a fancy pair of shoes, this is a special birthday and it only happens once a year, it will be a memorable event for him.
If I were your ex, I would appreciate a heads-up with enough advance notice for me to save up if money is somewhat tight, but I don't see why he'd object, unless, like I said, he is strapped for money. How much notice are you giving him? Not much it seems, if you have already made reservations. Hopefully, if he doesn't agree, you will still be able to afford the party, but in the future, I'd give maybe a month's notice, so he can't claim he didn't have enough time to save up and was blindsided with this expense. Good luck, I hope your ex pays up and your son has a great time!