In this work, we analyze the influence of the alloy disorder (AD) scattering on the low-field hole mobility of Si1-xGex nanowires (NWs). To do it, the electrostatic description is achieved through a self-consistent solution of the Poisson equation and the six-band k⋅p method in the cross section of the NW. The momentum relaxation time approximation is used to calculate the hole mobility, including alloy disorder and phonon scattering mechanisms, and the use of approximations to calculate the overlap integrals for the scattering matrix elements is discussed. We study the influence of the alloy disorder scattering on the total mobility compared to the phonon contribution, for different values of the AD scattering parameter proposed in the literature, and analyze the performance of SiGe NWs as a function of the Ge molar fraction for both low and high inversion charge densities.