Summary

I have two cowboy hats, and can't hang them on nails or the existing have because they hurt the band on the inside, or deform the hat.

This part uses 2x 1/8" (pretty standard) picture hanging nails, which are hammered into the wall through the two holes, such that the tips of nails point 30 degrees downwards (fixed angle in the design this should be fine)

then, lay a hat on top of it and it holds! no strange creases, deformation, or band damage!