The best replacement for hats is caps.

The best alternatives to hats are rated as following:
★★★★★  caps
★★  visors
★★  cp9
★★  beanies
★★  fascinators
★  black hats
★  white hats
★  bump caps
★  bonnets
★  hats
★  snapbacks
★  helmets
★  hard hats
★  wigs
  sun visors
  kuma
  fitted
  top hats
  lids
  baseball hats
  flat caps

Your alternative for hats is not listed? Suggest!
Speaking about hats, one probably shouldn't forget about veils.

Other search terms related to hats and their ratings are:
★★★★★ veils
safety
You have in mind a companion for hats and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of hats in all years. Click on graph for more.
hats
caps
visors