The walk-around was not just used at the end of a minstrel show; in the minstrel show's early history it could be intercalated whenever the audience's attention needed to be focused on a particular act, and it could be enlarged into an act itself. It is an old theatrical device, enlarged upon by the minstrel companies, perhaps first called a 'walk-around' by "Cool" White, who is blamed by some for "Buffalo Gals."
There are several banjo tunes called walk-arounds, some may stem from the music played during that stage of the performance, but they may just be names applied to tunes by banjoists long after the minstrels heyday.

The walk-around became a fixture at the end of the first half of the show; the end-of-show 'walk-around developed later. This depended upon the particular minstrel troupe and which stage in the development of the shows you are talking about.

This is all digression; the walk-around question was raised regarding its attribution to African-American origins.