Beautiful but somewhat musty hats...salvageable?

Spray with Febreese and store in raw rice. Just an idea don’t know for sure.

Bring to a dry cleaners and ask for advice?

Second the dry cleaners. That came to mind right off.

You can also try enclosing them with a combination of clay based (clumping) kitty litter and baking soda (both of which absorb noxious smells).
FYI, Arm and Hammer brand already contains baking soda. But you can also add more.

However, if the smell is due to the growth of mold and you can’t spray or wet them down with bleach (the really sure way to kill off mold spores) you may be back to square one a while later.

But both cat litter and baking soda are pretty cheap so it’s worth a try.

Febreze will do nothing except disguise the smell by overcoming it with that horrendous perfumey chemical concoction they use. It will do nothing to eliminate the smell already there.and IMHO, Febreze really smells awful. Both baking soda and clay are natural products. Febreze is a bunch of noxious chemicals.

Vinegar will kill mold, but just putting the hats and bag in a plastic bag with vinegar won’t do the trick. You’ll need to rinse your items in a vinegar/water bath. The vinegar doesn’t need to be full strength, but it still needs to smell like vinegar. Then rinse again with plain water, then let dry. If the items have decorations that might bleed color, you’ll want to remove them and rinse them separately and let dry.