Given the current emphasis on accurate Computational Fluid Dynamics (CFD) modeling of cardiovascular flows, which encompasses realistic geometries and cardiac waveforms, it is necessary to revisit the conventional wisdom regarding the influences of non-Newtonian effects. In this study, patient-specific reconstructed 3D geometries, viscosity data, and venous pulses post dialysis access surgery are used as the basis for the hemodynamic simulations. Rheological analysis of the viscometry data initially suggested that the correct choice of constitutive relations to capture the non-Newtonian behavior of blood is important because the End Stage Renal Disease (ESRD) patient cohort under observation experience drastic alteration in whole blood viscosity throughout the hemodialysis treatment. Various constitutive relations have been tested for this purpose, namely Quemada and Casson. Because of the specific interest in the onset of Neointimal Hyperplasia (NH) and stenosis in this study, particular attention is placed on differences in Wall Shear Stress (WSS) as that drives the adaptation process that leads to geometric modifications over time. The results exhibit no major differences in the flow field and general flow characteristics between a non-Newtonian simulation compared to a corresponding identical Newtonian simulation. It is found that geometric features of patient-specific geometries have greater influence on the WSS distribution within the numerical domain.