I'll hallucinate that you think the new girl is going to be into you and your wife equally. As mentioned above, that's not necessarily going to be the case. Indeed, it will likely *not* be the case.
So, I'll suggest asking the new girl what sort of relationship she wants to have with *you* and what sort of relationship she wants to have with *your wife*. What she wants could be very different, especially if she has a strong mistrust of men to work through.
When speaking of various forms of non-monogamy...it ain't poly if you're just fucking around.
While polyamory, open relationships, and swinging are all distinctly different approaches to non-monogamy, they are not mutually exlusive. Folks can, and some do, engage in more than one of them at a time--and it's all good.