The integral equation theory of pure liquids, combined with a new "scaling approximation" based on a corresponding states treatment of pair correlation functions, is used to evaluate approximate structure factors for colloidal fluids constituted of uncharged particles with polydispersity in size and energy parameters. Both hard sphere and Lennard-Jones interactions are considered. For polydisperse hard spheres, the scaling approximation is compared to theories utilized by small angle scattering experimentalists (decoupling approximation and local monodisperse approximation) and to the van der Waals one-fluid theory. The results are tested against predictions from analytical expressions, exact within the Percus-Yevick approximation. For polydisperse Lennard-Jones particles, the scaling approximation, combined with a "modified hypernetted chain" integral equation, is tested against molecular dynamics data generated for the present work. Despite its simplicity, the scaling approximation exhibits a satisfactory performance for both potentials, and represents a considerable improvement over the above mentioned theories. Shortcomings of the proposed theory, its applicability to the analysis of experimental scattering data, and its possible extensions to different potentials are finally discussed.