  The anisotropies of the Stochastic Gravitational-Wave Background (SGWB)
produced by merging compact binaries constitute a possible new probe of the
Large-Scale Structure (LSS). However, the significant shot noise contribution
caused by the discreteness of the GW sources and the poor angular resolution of
the instruments hamper the detection of the intrinsic anisotropies induced by
the LSS. In this work, we investigate the potential of cross-correlating
forthcoming high precision measurements of the SGWB energy density and the
Cosmic Microwave Background (CMB) lensing convergence to mitigate the effect of
shot noise. Combining a detailed model of stellar and galactic astrophysics
with a novel framework to distribute the GW emitters in the sky, we compute the
auto- and cross-correlation power spectra for the two cosmic fields, evaluate
the shot noise contribution and predict the signal-to-noise ratio. The results
of our analysis show that the SGWB energy density correlates significantly with
the CMB lensing convergence and that the cross-correlation between these two
cosmic fields reduces the impact of instrumental and shot noise. Unfortunately,
the S/N is not high enough to detect the intrinsic SGWB anisotropies.
Nevertheless, a network composed of both present and future generation GW
interferometers, operating for at least 10 yrs, should be able to measure the
shot noise contribution.
