We systematically study the pump-wavelength dependence of terahertz pulse generation in thin-film spintronic THz emitters composed of a ferromagnetic Fe layer between adjacent nonmagnetic W and Pt layers. We find that the efficiency of THz generation is essentially at for excitation by 150 fs pulses with center wavelengths ranging from 900 to 1500 nm, demonstrating that the spin current does not depend strongly on the pump photon energy. We show that the inclusion of dielectric overlayers of TiO2 and SiO2, designed for a particular excitation wavelength, can enhance the terahertz emission by a factor of of up to two in field.