Puppet hats! I hope this covid-era tutorial helps make the making easier. I made it to go with the emu kits. If you missed the kits, you can certainly find the materials.  And, of course, think about making your own wild puppet hat design.

About hat fitting:
Human head sizes vary a lot, costume felt hats not so much. If your hat is too big; try putting it on top of a hat that fits you or add (hot glue) material to the inside (like a folded up bandana, foam, pipe insulation) or if it's really big, cut the hat in half and slide it to size and glue. You could add a chin strap, too.  If your hat is too small, slice the back and cover the gap with cardboard. Cereal box cardboard is good for that job.