Saying no is instantly a negative thing by the literal definition of "no". So however you ask your staff it won't matter, they will be uncomfortable at the event or uncomfortable saying no.
I'm a new SWE Manager and I've been thinking alot about power dynamics since I got promoted. You would think that you can just tell you reports "hey you can be honest with me and speak your mind", but the difficult part about that is no one will take you at your word when you say that.
I'm still working it out but one thing I've found that helps is to crack some jokes with my reports. Like the other day I was having a one on one with a report where they were saying that they didn't like how ClientX was doing ThingY on ProjectZ. I could tell by his tone that he was trying to gauge my reaction before continuing, I interjected with a light joke about said client, basically telling him that I completely agreed with his sentiment. From there I noticed that things got much lighter and he was able to speak his mind more about the issue.
Was that the right approach? Who the fuck knows.
In my first time leading a team, a few months in one of the people on my team who I had known personally from before pulled me aside and basically said "listen, I know you, and I know that you are a sarcastic person and can understand it. But everyone else kind of thinks you're an asshole". Still very thankful that they pointed that one out to me.
"You're being disrespectful."
"The team's productivity and morale is more important than you."
The majority of us understand we're not fully rational and treading ground as if that's the case, is exactly how one ruins their chances. There's a far lower risk in faking things than there is trying to be honest and hoping the opposite party is not affected by negativity, both consciously and subconsciously.
The number of superiors who say similar and do get affected subconsciously far outnumber those who aren't affected. Most of us are playing a game of Poker, not a game of DnD.
Of course not, because of the SNAFU Principle: "True communication is possible only between equals, because inferiors are more consistently rewarded for telling their superiors pleasant lies than for telling the truth."
If I'm working for you, you are not my equal. You might be my superior in the organizational sense, because you have the power to demand I be fired if I push you hard enough. You are also my inferior in that you can't meet your KPIs without my cooperation. Under no circumstances will I tell you the plain, unvarnished truth. It isn't what you want to hear, especially if you've got senior managers or clients breathing down your neck. Shit doesn't just roll downhill in the Army.
You don't want to hear that it is flat-out impossible to come to me on Friday afternoon with a feature request that must be in production by the following Monday. Instead, I'd tell you that it can be done, but I'll expect time and a half for all of the overtime I'll be working that weekend, and it will probably be buggy because the requirements were scribbled on a fucking bar napkin and I probably won't have time to test it properly. You won't like that either, but at least you'll have the basis for a rough cost-benefit analysis you can present to your bosses to ask them, "How badly do you want this done in the current timeframe?"
I've also become a manager in recent months, and have had to think a lot about this. The approach I've mostly gone with is to try to be vulnerable and open about my own issues of the sort that I would want my reports to share. In the hope that they will reciprocate. It's hard to tell for sure, but that seems to have worked reasonably well.
I'd just caution you that... If you wanna bark up that tree you better be prepared to hear what they have to say. It might not be something you actually want to hear. And you're both going to have to deal with the fallout.
Or maybe they understand completely?
I sometimes organize dinners for my team (it's France after all). People can freely come or not and there is always someone who does not come. This someone changes all the time and nobody is keeping count.
I know my team inside out and, believe me, they will say when something pisses them off. Clearly. The dinners are not one of these things.