This communication presents an efficient technique for self-term evaluation of the uniform current vector potential integrals which often arise in certain cylindrical wire method of moments formulations. Simple approximating functions, derived from the application of numerical interpolation routines, are introduced that may be used in place of other more complicated techniques for evaluation of these integrals. In particular, this communication will focus on the development of these approximating functions for application in the moderately thick wire regime, where the reduced kernel approximation associated with thinner wires is no longer valid. It is shown that these proposed functions offer reasonably good accuracy over a wide range of wire segment lengths and radii.