Here is what I tried. I began along the cast on edge at the edge of my swatch. I inserted the small silver dpn into the bind off loops ( I had them on the needle the wrong way so when I worked them I did it though the back loop, if you did them right you wouldn't need to do that). So I didn't do a regular "pick up and knit", just ran the needle through the stitches. I had used a long tail cast on and purled the first row of my swatch. If your case is different you will have to experiment to see what looks best.
Then I cast on 6 stitches (random number) to make the width of the band. I knitted across the first 5 stitches and then with the RS facing slipped the last stitch knit wise, then I slipped the first of the stitches on the silver needle that I had picked up.
This picture shows how I slipped the stitch off the bottom edge of the swatch:
After I had that stitch slipped (also knitwise if it was on the needle right and straight on purlwise, behind the needle with it the way I had them) I completed a slip, slip, knit. So I had the last stitch of the 6 band stitches slipped then the one from the edge, then knit them together like a SSK. Now turn and knit back across the 6 stitches, turn and knit 5 and repeat the joining SSK. I recommend a smaller needle than you used for the sweater by at least 2 sizes because you will have more rows because you have to work back and forth to make the band. My sample was all on the same size needle that I knit the "sweater" swatch from.
This picture shows how it looks from the right side. The silver needle is holding the stitches from the edge. This is showing it upside down from the way it was worked.
I don't think you (or should I say I) could work the band around the corner and on up the front of the mini sweater piece. I think I would pick up stitches along the front including the edge of the bottom band and work the front band in a similar way. I haven't tried it yet and don't know how it will look though.
Here is one more picture of what I was getting.
Maybe this will give you an idea of how you might proceed.