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Charged Lepton Flavour Violating (cLFV) decays constrain the relationship between the neutrino and the scalar sectors of the Grimus-Neufeld model (GNM), an appealing minimal model of neutrino masses. It turns out, that in the scenario, where the seesaw scale is lower than the electroweak one, cLFV is completely defined by the new Yukawa interactions between the additional single heavy Majorana neutrino, the second Higgs doublet and the lepton doublets. Therefore, we derive a useful parameterization for the Yukawa couplings which reproduces by construction the correct PMNS matrix and the correct neutrino masses for both Normal and Inverted ordering at one-loop level. We embed this scenario in the $\texttt{FlexibleSUSY}$ spectrum-generator generator to perform parameter scans. Focusing on the tiny seesaw scale, we show that current $μ\to eγ$ limits provide significant constraints on the scalar sector, and we evaluate the impact of future cLFV $τ$-decay searches for the cases of discovery or non-discovery. The tiny seesaw scale makes the neutrino sector and the cLFV processes in the GNM similar to the scotogenic and the scoto-seesaw models, so we provide constraints for these models as well.