No one has to ask fiddler David Greely twice if he’s excited about the new Grammy category for zydeco and Cajun music recordings. Greely, co-founder of two-time Grammy nominees Steve Riley and the Mamou Playboys, thinks the category is long overdue.

“We’re no less deserving of our own category than other fine forms of music that get a Grammy every year,” he says. “We don’t have to wait every 10 to 20 years,...