Abstract: The extragalactic gamma-ray and neutrino emission may have a contribution from dark matter (DM) annihilations. In the case of discrepancies between observations and standard predictions, one could infer the DM pair annihilation cross section into cosmic rays by studying the shape of the energy spectrum. So far all analyses of the extragalactic DM signal have assumed the standard cosmological model (ACDM) as the underlying theory. However, there are alternative DM scenarios where the number of low-mass objects is significantly suppressed. Therefore the characteristics of the gamma-ray and neutrino emission in these models may differ from ACDM as a result. Here we show that the extragalactic isotropic signal in these alternative models has a similar energy dependence to that in ACDM, but the overall normalisation is reduced. The similarities between the energy spectra combined with the flux suppression could lead one to misinterpret possible evidence for models beyond ACDM as being due to CDM particles annihilating with a much weaker cross section than expected.