Back in 1966, Button World released a series of pins of the DC and Marvel Superheroes. Hawkman got his own badge as well. The pin is about 3cm wide and features the art of Murphy Anderson. The badge has become a collector's item over the years. You can see them sold anywhere from $10 to over $100.
I've managed to collect 11 of the badges over the years.
Different auction and other sites have these buttons for sale so you might be able to find one of your favorite superhero for a reasonable price. Happy hunting!