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This paper proposes an efficient potential and viscous flow decomposition method for wave-structure interaction simulation with single-phase potential flow wave models and two-phase Computational Fluid Dynamics (CFD) solvers. The potential part - represents the incident waves - is solved with spectral wave models; the viscous part - represents the complementary perturbation on the incident waves - is solved with the CFD solver. This combination keeps the efficiency and accuracy of potential theory on water waves and the advantage of two-phase CFD solvers on complex flows (wave breaking, flow separation, etc.). The decomposition strategy is called Spectral Wave Explicit Navier-Stokes Equations (SWENSE), originally proposed for single-phase CFD solvers. Firstly, this paper presents an extension of the SWENSE method for two-phase CFD solvers. Secondly, an accurate and efficient method to interpolate potential flow results obtained with the High Order Spectral (HOS) wave model on CFD mesh is proposed. The method is able to reduce the divergence error of the interpolated velocity field to meet the CFD solver's needs without reprojection. Implemented within OpenFOAM, these methods are tested by three convincing verification, validation and application cases, considering incident wave propagation, high-order loads on a vertical cylinder in regular waves, and a Catenary Anchor Leg Mooring (CALM) buoy in both regular and irregular waves. Speed-ups between 1.71 and 4.28 are achieved with the test cases. The wave models and the interpolation method are released open-source to the public.