I have "cookie" ornaments for my Christmas tree that I made at least 15 years ago that I still hang! They are not edible though. I mixed equal parts of applesauce, elmer's glue, and cinnamon, then rolled out the "dough" on saran wrap, cut out the shapes with a cookie cutter, and left to dry (it took a couple of days). Then I decorated them. Make sure you poke a hole for the hanger before they dry completely. They smelled really strongly of cinnamon for quite a few years. They still have a subtle scent. I never had issues with bugs/mice. etc. Maybe you could use this formula for your cookie base?
If you wanted to use the cookie base you have the recipe for, couldn't you simply coat the decorated cookies with a clear glue and allow them to dry? I would imagine that would preserve them quite well, and keep any critters away.
Hope this helps.