  The search for a particle dark matter signal in terms of radiation produced
by dark matter annihilation or decay has to cope with the extreme faintness of
the predicted signal and the presence of masking astrophysical backgrounds. It
has been shown that using the correlated information between the dark matter
distribution in the Universe with the fluctuations of the cosmic radiation
fields has the potential to allow setting apart a pure dark matter signal from
astrophysical emissions, since spatial fluctuations in the radiation field due
to astrophysical sources and dark matter emission have different features. The
cross-correlation technique has been proposed and adopted for dark matter
studies by looking at dark matter halos (overdensities). In this paper we
extend the technique by focusing on the information on dark matter distribution
offered by cosmic voids, and by looking specifically at the gamma-ray dark
matter emission: we show that, while being underdense and therefore producing a
reduced emission as compared to halos, nevertheless in voids the relative size
of the cross-correlation signal due to decaying dark matter vs. astrophysical
sources is significantly more favourable, producing signal-to-background ratios
$S/B$ (even significantly) larger than 1 for decay lifetimes up to $2 \times
10^{30}$ s. This is at variance with the case of halos, where $S/B$ is
typically (even much) smaller than 1. We show that forthcoming galaxy surveys
such as Euclid combined with future generation gamma-ray detectors with
improved specifications have the ability to provide a hint of such a signal
with a predicted significance up to $5.7\sigma$ for galaxies and $1.6\sigma$
for the cosmic shear. The bound on the dark matter lifetime attainable
exploiting voids is predicted to improve on current bounds in a mass range for
the WIMP of $25\div900$ GeV.
