That have been baked on a stick, but not decorated. Do you thaw them in an airtight container or out in the open?

Just thaw them in the package. you can also thaw them overnight in the fridge.

Funny, I just made 200 cookies on a stick and froze them. When I thaw them I take them right from the freezer and put them out on cooling racks. They're thawed and ready to decorate in about an hour.