Driven by low-carbon mandates, hybrid power vessels integrating diesel, battery, shore-power, and photovoltaic vessel (PV) systems are emerging as a key green shipping pathway. However, operation scheduling is essentially complex due to the integration between supply-side routing and load-side energy dispatch, which is compounded by multi-dimensional uncertainties in PV generation, port-grid loads, and feeder delays. To address this, we formulate a unified two-stage robust optimization model. The objective is to simultaneously minimize operating costs and enhance port-grid friendliness by coordinating on-board energy management and shore-power interactions. In detail, the first stage determines routing and sailing speeds, while the second stage allocates multi-source power under a worst-case budgeted polyhedral uncertainty set. A piecewise-linearization scheme handles the cubic speed–power relation, rendering a tractable mixed-integer linear programming problem. The problem is efficiently solved via a tailored Benders decomposition algorithm, utilizing a genetic-algorithm warm-start to substantially accelerate convergence. Validated on three real-world networks via 1000 Monte Carlo scenarios, the proposed model reduces mean operating costs by 20.2–23.5% and suppresses cost variance by over 60% compared to deterministic approaches.