This study investigates the magneto hydrodynamic (MHD) boundary layer flow and double-diffusive heat and mass transfer characteristics of a hybrid nanofluid composed of silver (Ag) and magnesium oxide (MgO) nanoparticles dispersed in water over a vertically oriented cone with convective surface heating. The novelty of the work lies in the simultaneous incorporation of Cattaneo–Christov heat and mass flux theories to model non-Fourier heat conduction and non-Fickian mass diffusion in the presence of hybrid nanofluid effects, space-dependent internal heat generation/absorption, and first-order chemical reaction. A uniform transverse magnetic field is applied to examine electromagnetic control of the transport processes. The governing nonlinear partial differential equations describing continuity, momentum, energy, and concentration are transformed into a coupled system of nonlinear ordinary differential equations using suitable similarity transformations. The resulting system is solved analytically through the Optimal Homotopy Asymptotic Method (OHAM). The results demonstrate that increasing the magnetic parameter significantly suppresses the velocity field due to the enhanced Lorentz force, while simultaneously elevating the temperature distribution because of resistive heating effects. The inclusion of Ag–MgO hybrid nanoparticles substantially enhances thermal performance, yielding nearly 31.2% improvements in heat transfer rate compared with the base fluid. Furthermore, thermal and solutal relaxation parameters delay heat and mass diffusion, thereby reducing thermal and concentration boundary layer thicknesses. Stronger chemical reaction effects markedly decrease concentration profiles through accelerated species consumption. These findings highlight the potential of hybrid nanofluids in advanced cooling technologies, nuclear energy systems, and high-performance thermal management applications.