Instead of the button-on strap, I looped three doubled pieces of yarn through each of the hat's corners and braided the six ends to form sturdy strings to tie the hat on with. The strings will obviously make this hat adjustable, too (even more so than the button-on strap).
This hat will be available at the upcoming November craft show unless someone claims it earlier than then. I would like to sell the hat and shoes as a set, but will, of course, be open to selling them individually.