Visor

A visor is either a special hat or the part of the hat that usually hangs over the forehead to protect the eyes from the sun.

In mainstream Smurfs media, Handy wears a Smurf hat with a visor while Reporter wears one over his Smurf hat in the cartoon show. In the EMPATH: The Luckiest Smurf story series, Printer wears the latter style of hat.