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In this third paper of a series on radio weak lensing for cosmology with theSquare Kilometre Array, we scrutinise synergies between cosmic shearmeasurements in the radio and optical/near-IR bands for mitigating systematiceffects. We focus on three main classes of systematics: (i) experimentalsystematic errors in the observed shear; (ii) signal contamination by intrinsicalignments; and (iii) systematic effects due to an incorrect modelling ofnon-linear scales. First, we show that a comprehensive, multi-wavelengthanalysis provides a self-calibration method for experimental systematiceffects, only implying <50% increment on the errors on cosmological parameters.We also illustrate how the cross-correlation between radio and optical/near-IRsurveys alone is able to remove residual systematics with variance as large as0.00001, i.e. the same order of magnitude of the cosmological signal. This alsoopens the possibility of using such a cross-correlation as a means to detectunknown experimental systematics. Secondly, we demonstrate that, thanks topolarisation information, radio weak lensing surveys will be able to mitigatecontamination by intrinsic alignments, in a way similar but fully complementaryto available self-calibration methods based on position-shear correlations.Lastly, we illustrate how radio weak lensing experiments, reaching higherredshifts than those accessible to optical surveys, will probe dark energy andthe growth of cosmic structures in regimes less contaminated by non-linearitiesin the matter perturbations. For instance, the higher-redshift bins of radiocatalogues peak at z~0.8-1, whereas their optical/near-IR counterparts arelimited to z<0.5-0.7. This translates into having a cosmological signal 2 to 5times less contaminated by non-linear perturbations.

SKA Weak Lensing III: Added Value of Multi-Wavelength Synergies for the Mitigation of Systematics