The WallDYN package has recently been applied to a number of tokamaks to self-consistently model the evolution of mixed-material plasma facing surfaces. A key component of the WallDYN model is the concentration-dependent surface sputtering rate, calculated using SDTRIM.SP. This modeled sputtering rate is strongly influenced by the surface binding energies (SBEs) of the constituent materials, which are well known for pure elements but often are poorly constrained for mixed-materials. This work examines the sensitivity of WallDYN surface evolution calculations to different models for mixed-material SBEs, focusing on the carbon/lithium/oxygen/deuterium system present in NSTX. A realistic plasma background is reconstructed from a high density, H-mode NSTX discharge, featuring an attached outer strike point with local density and temperature of 4e20 m^-3 and 4 eV, respectively. It is found that various mixed-material SBE models lead to significant qualitative and quantitative changes in the surface evolution profile at the outer divertor, with the highest leverage parameter being the C-Li binding model. Uncertainties of order 50%, appearing on time scales relevant to tokamak experiments, highlight the importance of choosing an appropriate mixed-material sputtering representation when modeling the surface evolution of plasma facing components. These results are generalized to other fusion-relevant materials with different ranges of SBEs.