The χ(3) nonlinear properties of slotted crystalline silicon photonic waveguides filled with third-order nonlinear materials (NM) are studied by calculating the effective nonlinear susceptibilities associated to the silicon and cladding material, respectively. The adopted approach circumvents the assumptions that the introduced NM dominates the nonlinear behavior of the slotted waveguide and that strong light confinement in the slot allows neglecting the two-photon absorption (TPA) process in the silicon rails. Optimization of the geometry of silicon-slotted waveguides is performed on the basis of the nonlinear figure of merit (FOM(TPA)) of the guided mode, which is related to the balance between the Kerr and the TPA effects, allowing to reach a FOM(TPA)=4.25. The obtained results reveal the importance of properly choosing the waveguide width of the silicon rails in order to minimize the TPA effect even by tolerating a reduced overall nonlinearity.