The shadows of black holes encode significant information about the properties of black holes and the spacetime surrounding them. So far, the effects of dispersive media, such as plasma, and relativistic aberration on the propagation of light around compact objects have been treated separately in the literature. In this paper, we will employ the Konoplya, Stuchlik, and Zhidenko family of stationary, axially symmetric, and asymptotically flat metrics to describe the spacetime around rotating black holes. We will study how the parameters of the black hole, the chromatic effects resulting from the presence of a nonmagnetized, pressureless plasma environment, and the effects of relativistic aberration of a moving observer modify the morphology of the shadow.