The edit to your question's title actually suggests a possible route to make your introduction "more inviting", which I am assuming means that you don't mind explaining a bit for folks who aren't familiar with polyamory.
Part of the awkwardness of "my wife and her boyfriend" is, as others have mentioned, that this leaves ambiguous what your relationship to the other man is. Of course seeing the three of you interact after the introduction will probably indicate the correct relationship (you aren't angry or jealous and so forth), but at the point of that initial introduction the only way to clarify any of the questions running through people's heads would be to ask directly, which is likely to feel too nosy to most folks.
So, instead, consider saying something like
Ah, this is my wife Mrs. X! And this is my metamour Y.
This situates both people in relation to you, which makes sense when you are making the introduction and should help clarify the congeniality of your mutual relationship. This is similar to the difference between "this is my wife, her sister's daughter, and my wife's father" versus "this is my wife, my niece, and my father-in-law"—it's subtle, but puts you more firmly within the web of relationships, rather than as a hanger-on.
Of course, metamour is (right now) a somewhat obscure* term outside of poly communities, but that obscurity can actually help you here.
- First, those who know what it means will instantly understand, and will be able to respond appropriately.
- Second, it's rare enough that it is reasonable for people to ask for an explanation if they want to. Where "So...is that OK with you?" and other clarifying questions about Y's boyfriend status might be perceived as rude and nosy, a response like "I don't think I've heard that term before" or "I'm sorry, could you repeat that?" is quite neutral and gives you an opening to explain in as much or as little detail as you feel is appropriate.
There will still be folks who just give you a glazed smile and nod, but with this approach you will have been honest and open about your relationship and have left the door open for the other person to inquire further.
*In spite of the term's overall obsurity, the root "amour" is probably transparent enough that some folks will figure out that you mean some kind of romantic relationship. Whether this increases or decreases any awkwardness will depend on the individual you're addressing, but I wouldn't expect it to be greater than the awkwardness you're experiencing now.