Hybrid nanofluids have gained significant attention due to their enhanced thermal conductivity, making them valuable in industrial cooling, biomedical devices, tribology, and renewable energy systems. However, the impact of hybrid nanofluids exhibiting non-Newtonian behavior, modeled using the Ellis rheological formulation, which better represents the shear-thinning properties of complex fluids, on flow and heat transfer over a stretching/shrinking cylinder under thermal radiation and suction/injection remains underexplored. This study addresses this gap by developing a mathematical model incorporating molybdenum disulfide (MoS2) and graphene oxide (GO) in a water-carboxymethyl cellulose (CMC) base. The present mathematical model is formulated using a set of partial differential equations, which are transformed into non-dimensional ordinary differential equations through similarity transformations and subsequently solved computationally using the bvp4c function. Graphical representations are employed to investigate the influence of multiple factors on velocity, temperature, skin friction coefficient, and the local Nusselt number. The results indicate that an increase in the Forchheimer number, magnetic parameter, velocity slip, porosity, and suction/blowing parameter results in a reduction in velocity profiles. Also, as the Eckert number, radiation parameter, and curvature parameter elevate, the temperature profiles display an upward shift. Moreover, a notable 20.03% decrease in the skin friction coefficient is observed when the porosity parameter increases from 0.5 to 2.0. These findings contribute to optimizing hybrid nanofluid applications in energy-efficient thermal management and advanced engineering systems.