High-energy X-ray radiation poses significant risks to human health and sensitive electronics, which necessitates the development of lightweight and multifunctional shielding materials for aerospace, medical, and defense applications. This study introduces an innovative approach by developing Elium®-based thermoplastic nanocomposites reinforced with polyacrylonitrile (PAN) nanofibers doped with silver (Ag) and silicon carbide (SiC) nanoparticles. The goal is to enhance mechanical performance, thermal stability, and X-ray attenuation capability while maintaining recyclability and processability. For this purpose, the nanofibers were produced using electrospinning, and nanocomposites were fabricated through resin impregnation followed by compression molding. The mechanical properties were evaluated through tensile testing, thermal stability was assessed through thermogravimetric analysis (TGA), and X-ray attenuation performance was determined using an X-ray transmission setup. The results demonstrate that hybrid Ag-SiC nanoparticle doping led to a 52% increase in tensile strength and a 15% improvement in strain compared to neat Elium®. Additionally, Ag-doped composites exhibited a 30 °C higher degradation onset temperature, indicating superior thermal stability. X-ray attenuation tests confirmed a 25% enhancement in linear attenuation coefficients for hybrid composites, making them highly effective for radiation shielding applications. These findings highlight the potential of Elium®-based nanocomposites as high-performance, lightweight, and eco-friendly alternatives to conventional shielding materials. Their enhanced multifunctional properties position them as promising candidates for aerospace, defense, and healthcare applications, contributing to safer and more sustainable engineering solutions.