Usage of without in conjunction with within

"There is no world without Verona walls." Shakespeare, "Romeo and Juliet."

It is archaic, or very nearly so. In my experience "without" in the sense of "outside" is only used today when coupled with "within" (as in your example), and each time one gets the feeling that something that was written a long time ago is being quoted. That said, it is NOT tacky at all. I.e. it's okay to use it in polite company.

There is a school in Bristol called St Michael's on the Mount Without. This name is from the mid-15th century, https://en.wikipedia.org/wiki/St_Michael_on_the_Mount_Without. The sense is that the church was sited outside the city walls.

He has participated in numerous projects both from within the same department and from without. Although the sense of your line is clear, modern usage would probably be ...from within the same department and externally.