We present optimization models that simultaneously determine ship path, speed profile, and hybrid power system operations. Our approach integrates solar photovoltaics, shore power, batteries, and diesel generators while accounting for power balance, propulsion physics, and itinerary constraints. To optimize path while avoiding obstacles, e.g., land, shallow waters, or protected areas, the nonconvex navigable space is partitioned into convex, obstacle-free sets, which can be embedded into the optimization problem using disjunctive constraints. The convex sets also serve to evaluate the impact of spatially varying environmental conditions, such as solar irradiance, wind, and currents on energy efficiency. Four models that balance the tradeoff between model accuracy and computational burden differently are formulated as mixed-integer convex programs (MICPs), solvable to global optimality using off-the-shelf commercial solvers. Four numerical case studies based on the S-175 ship model and historical ERA5 and Copernicus Marine data show that the models reduce operating costs relative to a shortest-path constant-speed baseline. In a synthetic case subject to brief adverse environmental conditions, modelling the coupling between passage time and environmental conditions enables the ship to delay its passage through the affected region and yields savings of up to 16.89%. In real-data cases, joint path optimization yields average savings of 14.22% when navigating Gulf of St.Lawrence seasonal speed restrictions and 5.92% when exploiting favourable environmental conditions. When the shortest path is already optimal, all optimization-based methods yield similar savings (approx 1%), highlighting that the benefits of our models arise when environmental or operational conditions create opportunities for route adaptation.