Light propagation in Swiss cheese models of random close-packed Szekeres structures: Effects of anisotropy and comparisons with perturbative results

Light propagation in two Swiss cheese models based on anisotropic Szekeres structures is studied and compared with light propagation in Swiss cheese models based on the Szekeres models' underlying LTB models. The study shows that the anisotropy of the Szekeres models has only a small effect on quantities such as redshift-distance relations, projected shear and expansion rate along individual light rays. \newline\indent The average angular diameter distance to the last scattering surface is computed for each model. Contrary to earlier studies, the results obtained here are (mostly) in agreement with perturbative results. In particular, a small negative shift, $\delta D_A:=\frac{D_A-D_{A,bg}}{D_{A,bg}}$, in the angular diameter distance is obtained upon line-of-sight averaging in three of the four models. The results are, however, not statistically significant. In the fourth model, there is a small positive shift which has an especially small statistical significance. The line-of-sight averaged inverse magnification at $z = 1100$ is consistent with $1$ to a high level of confidence for all models, indicating that the area of the surface corresponding to $z = 1100$ is close to that of the background.