You shouldn't have to stop socializing with people during your weight-loss and dieting. Abstaining from drinks and eating beforehand are great ideas as is the veggie pizza. Still eat beforehand so you're not hungry and wanting to pig out, but have a small slice of the veggie pizza so you're also not missing out on the fun. Or just have a sample instead of the whole slice. And take forever to eat it if you're worried about people calling you out, so you always have some pizza on your plate. That's what I do with drinks at the bar so in the end, I only end up having one or two the whole evening.
You're right in saying it's just one day, because that's all it is. Everything is really ok in moderation, too. One small slice will have a tiny impact on your overall weight-loss, but being able to go and hang out with your friends will make you very happy. And you won't have to keep coming up with excuses as to why you have to skip out.
My friends are also slender, lean, and active so they don't need to watch what they eat at all. I haven't told them I'm dieting outright, but questions have come up about my habits. Like, I weighed out some pretzels as a snack for a snowboarding trip a few months back and wrote the weight on the baggie so I'd know how much I was eating if I ate half the bag, etc. Someone asked and I just shrugged it off as by saying "I'm trying to clean up my eating and this way it makes it easy to know how much I've had during the day." All they said was ok and moved on to another topic of conversation, as if it didn't even matter.
So if you don't want a stigma attached to your dieting if anyone asks, then don't call it dieting necessarily. There are many different things to say such as "I'm cleaning up my eating", "I'm watching what I put in my mouth", "I'm trying to eat more veggies and less junk" (even if that may not actually be the case), etc. While it's still dieting per se, it doesn't sound like it to some people and they might not see it as dieting but as being more healthy in general.