check an office supply store for the clip attacher shown at the martelli site. we use them all the time to clip bundles of paper too thick for staples. they come in several sizes.
i know martelli makes great products but i think the price for the refills is a bit ... er ... ummmm ... muchish.
for myself, i think the hair clips would be a more reliable way to attach the binding. i think the clippie thing would be clumsy to use on a sandwich of fabric and batting. the clips would also be more difficult to remove. they are designed to hold on for dear life.