Instead of using the old mini blind slats, hand sew small plastic rings to the places where the slats above have their holes. Thread the mini-blind string through the rings and tie at the bottom ring. OR glue/sew pockets using add'l liner fabric to hide slats. See PureOfFaith.blogspot.com in favorites.
Did someone say NO sew? Music to these ears! I've an entirely rational fear of sewing machines after having to pull a sewing machine needle out of the center of my mom's thumbnail. I thought we were both gonna pass out.