How are you going to do the corners? The reason for cotton binding is because you don't end up with too much bulk to sew over when doing corners. If you have extra, do up a small quilt square and try the velvet around the edge for binding it. If it's too bulky for mitered corners, how would rounded corners look? If doing rounded corners you may have to cut the strips on the bias. Good luck. I'm sure someone will be able to help. Some have done quilts with Minky and might have some pointers for doing the binding.