The Houston Press categorized Cockadoodledon't as a "atomic psychobilly album". According to PopMatters, the style of Cockadoodledon't is defined by the Legendary Shack Shakers' detours from the album's overall sound, which The Cleveland Scene said sounded like "if Tom Waits, Southern Culture on the Skids, and the brain trust behind Ren and Stimpy holed up in Johnny Cash's country cabin with an ample supply of beef jerky and moonshine". AllMusic said that the album was defined by "horror-movie vocals by frontman 'Colonel' J. D. Wilkes straight out of the Lux Interior school and a hardcore, ragged combination of frayed blues, twisted bluegrass and ornery swamp".
The Houston Press classified Cockadoodledon't as a "atomic psychobilly album". According to PopMatters, the style of Cockadoodledon't is characterized by the Legendary Shack Shakers' deviations from the album's overall sound, which The Cleveland Scene described as sounding like "if Tom Waits, Southern Culture on the Skids, and the brain trust behind Ren and Stimpy holed up in Johnny Cash's country cabin with an ample supply of beef jerky and moonshine". AllMusic stated that the album was defined by "horror-movie vocals by frontman 'Colonel' J. D. Wilkes straight out of the Lux Interior school and a hardcore, ragged combination of frayed blues, twisted bluegrass and ornery swamp".