Because it would be one thing if he means go with him to social events or locations that make him anxious to keep him company until he gets used to it again for a few times while he tries to talk to new people on his own. (esp if he's not been out and about in a long while and fees rusty)
But when I hear "wingman" I think of how some people use it. Like "go distract the uggo friend so I can rope off and bang the hottie." That's not so great sounding if he means it like the "pick up artist" people do. It's not in the military way like the one who protects the main pilot. More like the kinda predatory way.
Among my friends, male and female, your first paragraph is closer to what they mean when they ask me to be a wingman. Many of them are slightly introverted and have mild social anxiety so having me there makes it a little easier for them to warm up to the situation, because they have someone that will chat or get on the dance floor with them. On top of being supportive, the other wingman duty is to help make sure that it stays a safe space by having each other's back when it comes to aggressive creepy people that violate boundaries and have a hard time taking no as an answer or if a friend has too much to drink, making sure nothing skeezy happens to them because of their impaired judgment. Plus around here people tend to only socialize in small groups so if my friend that I'm with wants to talk to someone, it often means approaching a group so it's slightly less awkward to approach it with someone else that becomes an active part of the conversation. This is how I understood the OP's request for advice.
All that said, I don't have experience being a wingman in this type of situation, going out with my spouse to help her find a partner, however I have been in situations that are vaguely similar- hanging out with her and a metamour in social situations or being at some kind of gathering where one of us stumbles into what might be called a spontaneous encounter, unexpectedly liking someone and wanting the time/space to pursue it. So I can at least tell you how I handle these situations.
When it comes being social situations with a metamour, whether at home or in public, my general rule is to be a good host. I make the other person feel welcome, participate in the conversation, and also make sure to occasionally make graceful exits, staying away for a bit, so that they have some private time as well. So far, when we've done this, it's worked out extraordinarily well. For one, the metamour sees that I truly am supportive of what's going on which puts them at ease. It also demonstrates to my partner that I'm supportive of her as well. Plus I usually end up with a new friend as well because I typically get along very well with her metamours. The other nice thing is that I get the time and space I needed to meet people and have my own enjoyable night out. Take this with this grain of salt though- if you read enough posts here you'll find that a lot of folks prefer that their partner and the metamour have minimal to no interaction. This works for us because of who we are and how we see the world but it definitely isn't for everyone.
In the other situation, say we're at a party and she discovers that she wants to go off to talk with stranger-x, I encourage her, give them space, check in with her when she needs to, and generally go off on my own to talk to people and enjoy the party. So far it's worked out well for us. Once again though we're a bit more comfortable with being socially non-monogamous so it may not be for everyone.
Practically speaking, how would this work in your situation? How I read it, your husband is asking for someone to hold his hand as he's getting ready to leave the nest socially speaking. My first suggestion is a bit different from most the advice you've gotten or will get here- if all three of you are amenable to it, you and bear meet him at a bar for a couple of drinks with the understanding that at some point you and bear will be leaving so he'll be on his own. To reiterate something here, only do this if all three of you are ok with it. If everybody is ok with it, it will encourage him to talk to other people because he knows he's not leaving with you and it's more likely that people will respond to him because rather than seeing him there alone with his wife, they'll see him hanging out with a couple. However if any one of you wouldn't feel comfortable doing this, DON'T DO IT, as it will likely lead to someone having a meltdown in the near future. If going out as a group doesn't work, go out to the bar with him but as a friend rather than as his wife. By this make it clear up front that your body language and interactions are going to be friendly but not romantic. I'd also once again recommend making it clear that he's also not leaving with you, so maybe plan on leaving to go spend time with the BF or something.
It may seem harsh to set it up like that but honestly I see it as being appropriately supportive. He's basically asking for support, hand holding as it were, as he expands his social life. However it's also a situation where support can turn into enabling if he doesn't have an incentive to let go of your hand and dive into the water. Another benefit of doing it this way is that it makes him responsible for the outcome of his evening because if you stay there the entire night and he doesn't achieve the desired outcome there's a good chance he'll do what insecure people often do when things don't work out for them- try to flip it back on you.
If you choose to go to more organized social events, say poly meet-ups, going as a couple works but still set some limits on it, like maybe telling him you'll go a couple times with him to help him ease into it but after that he's on his own.
However there is also some consideration to telling him you love him, you're sorry he's struggling, that you want to support him in ways that you can but this isn't one of those ways so if he needs a wingman, consider asking a friend or three to tag along with him.