  We consider a Swiss Cheese model with a random arrangement of
Lema\^itre--Tolman--Bondi holes in $\Lambda$CDM cheese. We study two kinds of
holes with radius $r_b=50 h^{-1}$Mpc, with either an underdense or an overdense
centre, called the open and closed case, respectively. We calculate the effect
of the holes on the temperature, angular diameter distance and, for the first
time in Swiss Cheese models, shear of the CMB. We quantify the systematic shift
of the mean and the statistical scatter, and calculate the power spectra.
  In the open case, the temperature power spectrum is three orders of magnitude
below the linear ISW spectrum. It is sensitive to the details of the hole, in
the closed case the amplitude is two orders of magnitude smaller. In contrast,
the power spectra of the distance and shear are more robust, and agree with
perturbation theory and previous Swiss Cheese results. We do not find a
statistically significant mean shift in the sky average of the angular diameter
distance, and obtain the 95\% limit $|\Delta D_A/\bar{D}_A|\lesssim10^{-4}$.
  We consider the argument that areas of spherical surfaces are nearly
unaffected by perturbations, which is often invoked in light propagation
calculations. The closed case is consistent with this at 1$\sigma$, whereas in
the open case the probability is only 1.4%.
