The modeling of optical spectra of plasmonic nanoparticles via first-principles approaches is computationally expensive; thus, methods with high accuracy/computational cost ratio are required. Here, we show that the Time-Dependent Density Functional Theory (TDDFT) approach can be strongly simplified if only one s-type function per atom is employed in the auxiliary basis set, with a properly optimized exponent. This approach (named TDDFT-as, for auxiliary s-type) predicts excitation energies for silver nanoparticles with different sizes and shapes with an average error of only 12 meV compared to reference TDDFT calculations. The TDDFT-as approach resembles tight-binding approximation schemes for the linear-response treatment, but for the atomic transition charges, which are here computed exactly (i.e., without approximation from population analysis). We found that the exact computation of the atomic transition charges strongly improves the absorption spectra in a wide energy range.