Due to the unique electro-optical and thermal properties of atomically thin molybdenum disulphide (MoS$_2$), it has the potential to transport excess heat in advanced electronic devices to ensure the efficient working of the device. The present article investigates the impact of adding blade-shaped, brick-shaped, cylinder-shaped and platelet-shaped MoS$_2$ nanoparticles on the heat transport characteristics of viscoelastic ethylene glycol (EG). The time-dependent MHD non-Newtonian nanofluid flow is studied in the presence of temperature- and space-dependent heat source. The influence of different shapes of MoS$_2$ nanoparticles on entropy generation as well as heat transport characteristics of viscoelastic boundary layer flow is studied in depth by plotting comparative graphical profiles.This numerical study will help in achieving the enhancement of heat transfer rate in various industrial processes by opting a suitable nanoparticle shape and adjusting the associated parameters to an appropriate value as suggested by the study.