Efficient and lightweight heat sinks for microelectronic cooling are pivotal for developing energy-efficient next-generation devices with huge processing power and significant heat dissipation over small scales. Microchannel heat sinks offer a solution not only for cooling electronics but also in applications of energy harvesting, defense, and biomolecular dynamics. An accurate understanding of transport phenomena at these scales can guide us toward minimizing frictional losses and thermal entropy for efficient thermal management. In this study, we numerically investigate the hydrothermal characteristics of a wavy microchannel heat sink integrated with nanofluids containing nanoparticles of different shapes. Our primary objective is to enhance thermal performance by studying the effects of four distinct nanoparticle shapes: spheres, cylinders, platelets, and blades. The nanoparticle concentration is varied within the range of 0.02–0.08, while the Reynolds number is set within the laminar regime (200–800). By decoupling the different contributions to system entropy and exergy, we aim to gain insights into the underlying physics behind thermal performance enhancement using shape-based nanofluids. Our findings reveal a significant increase in convective heat transfer coefficient, up to 50.63%, as well as notable exergy savings of up to 65.56%.