The nonlinear characteristics of dust‐ion‐acoustic shock waves (DIASHWs) in a plasma consisting of charge‐fluctuating dust, inertial ions, and non‐Maxwellian electrons is examined. In particular, the electron velocity distribution function (VDF) is assumed to follow Kappa and Cairns distributions. In this regard, a reductive perturbation (RP) approach (in a weakly nonlinear limit) is used to derive the corresponding Burger's equation, and, from its solution, the effects of various physical parameters, for example, non‐thermal indices, number density, and temperature ratios, on the properties of shock waves are investigated. It is observed that the magnitude of the shock reduces as ion‐electron temperature ratio increases and vice versa. Furthermore, when the ion to electron (equilibrium) density ratio increases, the shock profile gets steepened. The resultant potential amplitude as well as the shock width is also shown to be strongly related to the spectral indices, namely κ and α in the case of Kappa‐ and Cairns‐distributed electrons, respectively. Hence, the potential distribution is strongly affected by the non‐thermal nature of the electron VDF. The relevant Maxwellian results are recovered in the limiting cases, namely κ → ∞ and α → 0. The present study will be useful in understanding the nonlinear propagation of DIASHWs in non‐thermal (space and laboratory) plasmas.