This is a nice, well-intentioned idea, but I have to suggest reconsidering.
In decades of office work, I observed this phenomenon again and again: there are always some people who want to get together socially with their coworkers during off hours (or even during working hours) and think the idea is fun. They don’t seem to notice that a whole other group of coworkers hate the idea. To them, that’s exactly the same as being asked to put in extra hours of work during their personal time. What they need is time away from their coworkers and not more time with them. Picnic, bowling, drinks, it doesn’t matter: to them it feels like an unwanted obligation, extra work time, and it’s the opposite of de-stressing.
Trying to “get everybody together” to do anything they’re not required to do by their job (whether it’s entertainment or volunteer work) is going to be a huge imposition on some, who probably will not say anything out loud because they don’t want to single themselves out. They may not even admit it if asked directly and privately, because they don’t want to label themselves as “not a team player”—a fast track to the next layoff cut list.
I know this because I was always one of those, and we seemed always to know each other. We would whisper quietly among ourselves, moaning about it and asking each other if we dared to miss the event. Usually we didn’t. And we always felt it as a huge burden.
In general I’ve observed that introverts try really hard to be understanding of extroverts, but extroverts don’t seem to realize that not everyone shares their enthusiasms. “Aw, come on, it’ll be fun!” (By nature the extroverts are always more conspicuous—and for that reason they often seem more numerous than they are.) Some job skills are not compatible with extrovert qualities, and those jobs truly are best filled by people who are quiet, focused, and perhaps even a bit socially isolated. And they don’t want to go to office social events.
The issue isn’t forcing people to attend. I know you will say “No one has to come who doesn’t want to.” Over the years those people have learned that it’s better not to admit they don’t want to. But it will still be painful for them.
I think the best thing is always to let people unwind in their own way, with the workplace as far from their minds as possible.