We present the results of an analysis aimed at probing the small-scale magnetic fields of M dwarfs observed with SPIRou, the nIR high-resolution spectro-polarimeter installed at the Canada-France-Hawaii Telescope, in the context of the SPIRou Legacy Survey. Our analysis relies on high-resolution median spectra built from several tens of spectra recorded between 2019 and 2022, and on synthetic spectra computed with the ZeeTurbo code for various combination of atmospheric parameters and magnetic field strengths. We pursue the efforts undertaken in a previous study and focus on 44 weakly to moderately active M dwarfs. We derive average magnetic field strengths () ranging from 0.05 to 1.15 kG, in good agreement with activity estimates and rotation periods. We found that including magnetic fields in our models has virtually no impact on our derived atmospheric parameters, and that a priori assumptions on the stellar surface gravity can affect our estimated . Our results suggest that small-scale magnetic fields account for more than 70 per cent of the overall average magnetic field for most targets whose large-scale fields were previously measured. We derived low magnetic fluxes for several targets in our sample, and found no clear evidence that decreases with increasing Rossby number in the unsaturated dynamo regime. We even identified counterexamples (GJ 1289 and GJ 1286) where the small-scale field is unusually strong despite the long rotation period. Along with similar results on the large-scale fields, our findings further suggest that dynamo processes may operate in a non-conventional mode in these strongly magnetic, slowly rotating stars.