This second segment of a two-part study investigates the numerical modeling of the Navier slip boundary condition at the contact line at the junction of free and solid surfaces, a key element in many natural and technological processes. The first segment introduced a method based on the cut-cell formalism. This second segment demonstrates how this simple formulation can be used to flexibly mix Navier, no-slip and free-surface boundary conditions near sharp interfaces described using a levelset representation. The study emphasizes a unified treatment of boundaries and interfaces that retains the simplicity of the original methodology without requiring further simplifying assumptions. To that end, a two-levelset approach is employed, with one levelset defining the solid wall and the other defining the free-surface. The spreading of a droplet over straight and circular walls for different contact angles is used as validation cases. The expected first-order accuracy in mass loss/gain is achieved, with the maximum error in mass conservation reaching 10% in the worst-case scenario.