Sunflower oil-based HBTPU/Ag and LTPU/Ag nanocomposites have been prepared by in situ catalytic reduction of a silver salt. The virgin polymer and their nanocomposites are soluble in various polar organic solvents and amenable for both solution-casting and hot pressing. XRD, TEM, and UV spectroscopic analyses ascertained well-dispersed, narrow-sized Ag nanoparticles. Tensile testing, dynamic mechanical, thermogravimetric, and DSC analyses showed desirable mechanical and thermal features with improvement upon incorporation of Ag nanoparticles and the presence of a hyperbranched component in the nanocomposites. RSM has been used to evaluate the catalytic efficacy of the nanocomposites.