The superconducting diode effect (SDE) enables nonreciprocal dissipationless transport when inversion and time-reversal symmetries are simultaneously broken. Rashba nanowires proximitized by conventional $s$-wave superconductors provide a minimal setting in which spin–orbit coupling and Zeeman fields generate asymmetric finite-momentum pairing. While most studies focus on the single-channel limit, which yields small diode efficiencies and requires multiple Zeeman-field components, realistic devices host multiple transverse subbands. Here, we investigate the SDE in multichannel Rashba nanowires with harmonic and rectangular quantum-well confinement using a self-consistent Bogoliubov–de Gennes formalism. Both geometries support asymmetric Fulde–Ferrell (FF) states that drive pronounced nonreciprocal supercurrents and stabilize a topological phase with Majorana zero modes, where the Cooper-pair momentum is controlled by an externally injected supercurrent. Pairing-susceptibility analysis shows that field-induced asymmetry favors directional Cooper pairing, explaining the nonmonotonic Zeeman-field dependence of the diode response. Harmonic confinement yields diode efficiencies of $\sim 60\%$ ({coupled channels}) and $\sim 55\%$ ({independent-channels}). In contrast, rectangular confinement sustains $\sim 60\%$ efficiency in both regimes and uniquely exhibits a tunable sign reversal in the coupled-channels case. Moreover, interchannel coupling allows a transverse Zeeman field alone to generate a finite diode response. These results establish the robustness of the SDE and topological FF states against transverse confinement variations, highlighting multichannel nanowires as powerful platforms for high-efficiency nonreciprocal transport and current-controlled topological superconductivity.