DHOST inflation models where deviations from a pure de Sitter background are induced by an axion-like potential can lead to large non-Gaussianities. We investigate the nature of non-Gaussianities in these models and compare to the results given by the Planck experiment. The overlap between the DHOST non-Gaussianities and the equilateral, orthogonal and local templates can be rendered arbitrarily small. On the other hand, this does not preclude DHOST models from showing large non-Gaussianities as exemplified by their reduced bispectrum. As a result, they could be probed by future experiments and also by a more thorough analysis of the existing Planck data.