I've often used satin as a binding on baby quilts. I even attached it to some quick fleece throws I made for the numerous grand and great grandkids (very quick as there were very many). I see them from time to time as they visit (still carrying them with them ... even the teenagers) and they are each and every one wearing very well.
I did the usual double-fold, but cut it generous at 2-1/2". Something else I do on the baby quilts is to attach a loop at each of the corners that the baby can hold onto with a couple fingers. They seem to love to fondle it as they're going to sleep.
I'd go for it. And I'd love to see pics when you're through.