I can't imagine you putting a very big button on a wrist band. I was wondering if a simple eyelet buttonhole wouldn't be your best bet. It works fine in garter stitch. Just knit to where you want the buttonhole, K2tog, YO. When you knit the next row/rnd, work the YO as a stitch. This will make a small buttonhole. To make one a little bigger with a more vertical look to it (there is another way to make a little bigger one that is horizontal), knit to where you want the buttonhole, YO twice, K2tog tbls. Next row work to the double yarn overs and knit the first one and let the second one drop.
I've never needed a vertical buttonhole but understand that it involves knitting to the buttonhole and using another piece of yarn on the other side of the buttonhole.
Using 3 rows of crochet makes a neat vertical buttonhole. sc across on one row, turn sc to where you want the buttonhole, ch 1 or 2, skip 1 or 2 sc, ch to end. turn and sc across all sts including the ch.