BENTONVILLE, Ark.—Now that it is home to a world-class art museum, a boutique hotel and a spate of fashionable restaurants, Joe Wilson says he worries that his hometown is losing its "hillbilly heritage."

So the 39-year-old construction project manager came up with an event designed to stave off big-city airs and remind locals that they still live in the Ozarks: The World Championship Squirrel Cook Off.

Entering...