So using one of her vintage chin straps as a guide, I created several wig chin straps with a white elastic cord and put them in the online catalog at
http://store.haircuttingfun.com/index.php?recid=447&maincat_id=4&subcat_id=10&page=1
Here's a photo of the wig chin strap as well:
They were created with big beautiful CDs in mind. Of course, if the strap is too long, it can always be knotted in the middle.