We study the evolution of temperature-dependent resistivity with controlled point-like disorder induced by 2.5 MeV electron irradiation in stoichiometric compositions of the "3-4-13" stannides, (Ca,Sr)3(Ir,Rh)4Sn13. Three of these cubic compounds exhibit a microscopic coexistence of chargedensity wave (CDW) order and superconductivity (SC), while Ca3Rh4Sn13 does not develop CDW order. As expected, the CDW transition temperature, TCDW, is universally suppressed by irradiation in all three compositions. The superconducting transition temperature, Tc, behaves in a more complex manner. In Sr3Rh4Sn13, it increases initially in a way consistent with a direct competition of CDW and SC, but quickly saturates at higher irradiation doses. In the other three compounds, Tc is monotonically suppressed by irradiation. The strongest suppression is found in Ca3Rh4Sn13, which does not have CDW order. We further examine this composition by measuring the London penetration depth, λ(T ), from which we derive the superfluid density. The result unambiguously points to a weak-coupling, full single gap, isotropic superconducting state. Therefore, we must explain two seemingly incompatible experimental observations: a single isotropic superconducting gap and a significant suppression of Tc by non-magnetic disorder. We conduct a quantitative theoretical analysis based on a generalized Anderson theorem which points to an unconventional multiband s +− -pairing state where the sign of the order parameter is different on one (or a small subset) of the smaller Fermi surface sheets, but remains overall fully-gapped.