Really, there is no such thing. Racketeers dressed well, period. Some guys like Capone wore fedoras. Dutch Schultz and the Bronx boys liked Homburgs. Albert Anastasia owned so many different types of hats that he was known as the Mad Hatter.
Its not so much the type of hat, though, as how you wear it and, more importantly, the color. Many dandies (ie gangsters) of the era wore the fedora in the "Hollywood" brim style, a la Capone in this mugshot:
The key, though, is the color: a pearl-grey fedora was the preferred color of the racketeer and gangsters of the era, regardless of the style of the hat:
Schultz and his counsel, Dixie Davis:
Mad Dog Coll and gang in pearl grey:
Unfortunately, the problem with pearl grey is that its tough to find. JJ Hatters here in NYC only do it special order via Borsalino.