While it is most likely possible, I'm not sure it would be the easiest route to go. I'm not sure if there is a difference in pivot size between the Wingman and the bigger tools that would have the small bit driver, but I believe there might be which would cause a big issue.
Would you be opposed to carrying a small swiss army knife? The combo tool with the phillips driver on tools like the rambler are known to be good for the small screws you're referring to, depending on how recessed of course.
Welcome to the forum by the way!