Irradiation with swift heavy ions of spherical Au nanoparticles confined within a silica matrix shapes them into prolate nanorods and nanowires whose principal axes are aligned along the beam direction. In the present paper, we investigate the role that is played by the initial nanoparticle size and concentration in this so-called ion-shaping mechanism. We have produced silica films wherein Au nanoparticles with average diameters of 15, 30, and 45 nm were embedded within a single plane and have irradiated these films at 300 K at normal incidence with 18, 25, and 54 MeV Ag ions. We demonstrate the existence of both threshold and saturation fluences for the elongation effects mentioned. The values of these critical fluences depend both on the ion energy and the initial nanoparticle size. Moreover, we show that 45 nm Au particles are not deformed when irradiated with 18 MeV Ag ions, such that this value corresponds to an energy threshold for the deformation process. As far as the influence of the nanoparticle concentration on the shaping characteristics is concerned, we have found that above the critical irradiation fluence, the deformation effect becomes very sensitive to the initial concentration of the nanoparticles.