We investigate a semidilute hard sphere colloidal suspension with no hydrodynamic interactions. The suspension undergoes a steady shear flow. In addition, a small constant external force induces a tagged particle flux. In order to determine the shear-dependent self-mobility matrix (relating the flux to the force) we construct the approximate solution to the two-particle Smoluchowski equation at contact, applying the induced source method, combined with a power expansion in the square root of the shear rate. We evaluate the self-mobility tensor numerically by means of Padé approximants for small and moderate shear rates.