The comparative assessment of the laser micro-drilling machinability of polymer matrix nanocomposites dispersed with conducting fillers of different carbon allotropes (carbon nanotube (CNT), graphite, and carbon black (CB)) to produce minimum taper and heat-affected zone (HAZ) has been first time reported in this article. The required composite specimens are synthesized via ultrasonicator-assisted compression molding method and characterized for their thermal, electrical, and mechanical properties. The central composite design-based response surface methodology (CRSM) is implemented for the planification of experimentation using a pulsed Nd:YAG laser and subsequent higher-order regression modeling of the desired performance indicators. The contemporary accelerated particle swarm optimization (APSO) technique and metaheuristic whale optimization algorithm (WOA) have been utilized to define optimum controllable process parameters (pulse frequency, cutting speed, lamp current, and air pressure) and the assortment of optimum conditions are justified by performing confirmatory tests. CNT-reinforced composite material exhibits superior tensile, hardness, and thermal properties whereas graphite-based polymer composite show good electrical conductivity. The most minor taper and HAZ values are observed in the laser micro-drilling of epoxy-based CNT and CB materials, respectively. The two swarm-based algorithms predict more accurate results for the desired output responses than the statistical CRSM, with the least errors compared to the values attained by the WOA. Optimal taper (with CNT/epoxy composite at 30 m/s cutting speed, 22.6 amp lamp current, 3 kHz pulse frequency, and 1 kg/cm2 air pressure) and HAZ (with CB/epoxy composite at 30 m/s cutting speed, 22.97 amp lamp current, 3 kHz pulse frequency, and 5 kg/cm2 air pressure) values obtained in the confirmatory test showed 15% and 12% errors, respectively, as compared to the predicted data in WOA.