A less-lethal shotgun/shotshell, 37mm, or 40mm cartridge for cooperative operation in less-lethal application with a non-centerfire shotgun or 37mm or 40mm launcher having an offset firing pin assembly, the shotgun, 37mm, or 40mm cartridge comprising: a cylindrical casing (106, 206) including a metallic case head (108, 208) proximate a first end, a hull proximate a second end, and an interior disposed within the casing between the first end and the second end, wherein the casing includes an exterior surface including a visible and/or tangible identifier indicating less-lethal capability; a non-centerfire propellant assembly (104, 204) including a non-centerfire primer assembly (150, 250) operatively positioned near a propellant charge; a recess defined within the metallic case head and including an opening centrally located proximate the first end of the metallic case head for receiving the non-centerfire primer assembly, the non-centerfire primer assembly located within the opening and including an annulus incendiary portion coaxially aligned with the casing, the annulus incendiary portion surrounding an inert portion centrally located within the first end of the metallic case head, wherein the annulus incendiary portion includes a primer compound and the inert portion is absent the primer compound; and a less-lethal projectile (156, 256, 356) affixed to and/or within the hull proximate the second end of the casing, wherein the propellant charge is capable of being ignited when the cartridge is loaded within the non-centerfire firearm and the annulus incendiary portion of the non-centerfire primer assembly is struck by the offset firing pin assembly; a space within the metallic case head and surrounding the annulus incendiary portion of the non-centerfire primer assembly to facilitate deforming the annulus incendiary portion of the non-centerfire primer assembly in response to the striking by offset firing pin assembly. a cylindrical casing (106, 206) including a metallic case head (108, 208) proximate a first end, a hull proximate a second end, and an interior disposed within the casing between the first end and the second end, wherein the casing includes an exterior surface including a visible and/or tangible identifier indicating less-lethal capability; a non-centerfire propellant assembly (104, 204) including a non-centerfire primer assembly (150, 250) operatively positioned near a propellant charge; a recess defined within the metallic case head and including an opening centrally located proximate the first end of the metallic case head for receiving the non-centerfire primer assembly, the non-centerfire primer assembly located within the opening and including an annulus incendiary portion coaxially aligned with the casing, the annulus incendiary portion surrounding an inert portion centrally located within the first end of the metallic case head, wherein the annulus incendiary portion includes a primer compound and the inert portion is absent the primer compound; and a less-lethal projectile (156, 256, 356) affixed to and/or within the hull proximate the second end of the casing, wherein the propellant charge is capable of being ignited when the cartridge is loaded within the non-centerfire firearm and the annulus incendiary portion of the non-centerfire primer assembly is struck by the offset firing pin assembly; a space within the metallic case head and surrounding the annulus incendiary portion of the non-centerfire primer assembly to facilitate deforming the annulus incendiary portion of the non-centerfire primer assembly in response to the striking by offset firing pin assembly.