It certainly would. How about an option of a bucket hat? I think that's what they're called, with the sun visor that goes all the way around.
Today 50 (2,500km), Montego. Fly (2,500km), Le Grande (7,000km), Vespa PX (200km), Vespa GTS250ie (46,000km), now looking at the world through Ruby coloured glasses on a Vespa GTV300ie Vie Della Moda.