  Since the advent of the accelerated expanding homogeneous universe model,
some other explanations for the supernova Ia dimming have been explored, among
which there are inhomogeneous models constructed with exact $\Lambda = 0$
solutions of Einstein's equations. They have been used either as one patch or
to build Swiss-cheese models. The most studied ones have been the
Lema\^itre-Tolman-Bondi (LTB) models. However, these models being spatially
spherical, they are not well designed to reproduce the large scale structures
which exhibit clusters, filaments and non spherical voids. This is the reason
why Szekeres models, which are devoid of any symmetry, have recently come into
play. In this paper, we give the equations and an algorithm to compute the
redshift-drift for the most general quasi-spherical Szekeres (QSS) models with
no dark energy. We apply it to a QSS model recently proposed by Bolejko and
Sussman (BSQSS model) who averaged their model to reproduce the density
distribution of the Alexander and collaborators' LTB model which is able to fit
a large set of cosmological data without dark energy. They concluded that their
model represents a significant improvement over the observed cosmic structure
description by spherical LTB models. We show here that this QSS model is ruled
out by a negative cosmological redshift, i.e. a blueshift, which is not
observed in the Universe. We also compute a positive redshift and the
redshift-drift for the Alexander et al.'s model and compare this redshift-drift
to that of the $\Lambda$CDM model. We conclude that the process of averaging an
unphysical QSS model can lead to obtain a physical model able to reproduce our
observed local Universe with no dark energy need and that the redshift-drift
can discriminate between this model and the $\Lambda$CDM model. For
completeness, we also compute the blueshift-drift of the BSQSS model.
