In this third paper of a series on radio weak lensing for cosmology with the Square Kilometre Array, we scrutinise the added value of synergies between cosmic shear measurements in the radio and optical/near-IR bands for the purpose of mitigating systematic effects. We focus on three main classes of systematics: (i) experimental systematic errors in the observed shear, (ii) signal contamination by intrinsic alignments, and (iii) systematic effects in the estimation of cosmological parameters due to an incorrect modelling of non-linear scales. First, we quantitatively illustrate how the cross-correlation between radio and optical/near-IR cosmic shear surveys will greatly help in mitigating the impact of the systematic effects in the shear measurement considered, opening also the possibility of using such a cross-correlation as a means to detect unknown experimental systematics. Secondly, we show that, thanks to polarisation information, radio weak lensing surveys will be able to mitigate contamination by intrinsic alignments, in a way similar but fully complementary to self-calibration methods, based on position-shear correlations. Lastly, radio weak lensing, reaching higher redshifts than those accessible to optical surveys, will probe dark energy and the growth of cosmic structures in r\'egimes less contaminated by non-linearities in the matter perturbations.
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