We theoretically present a flexible method to obtain dual-channel optical bistability (OB) in a coupled system consisting of a metallic nanoshell (MNS) and a carbon nanotube (CNT) nanomechanical resonator (NR) beyond the dipole approximation. The MNS is made of a metallic core and a dielectric shell. The results show that, the four-wave mixing signal is suppressed significantly due to multipole polarizations in comparison to that in the dipole approximation. Also, the four-wave mixing signal can be enhanced greatly with the exciton-phonon coupling strength g increasing. Especially, bistability phase diagrams plotted show that, for a given shell thickness, it is realizable to achieve one (or two) bistable region(s) by adjusting the pumping intensity (or the MNS-NR distance). In a strong exciton-plasmon coupling regime, OB can be switched from single-channel to dual-channel by only changing the dielectric shell thickness or the metallic core radius. This indicates that the system proposed can behave as a channel-tunable bistable switch. Our findings may have potential applications in various domains such as quantum communication and optical functional devices.