Evaluating the electromagnetic response of a thin wire is of significant mathematical complexity due to singularities in the integral equation describing the surface current. In our recent work, we investigate the response to a driving source on the wire, using the common "delta gap" model, in which a finite potential is maintained across an infinitesimal distance, thus producing a delta function in the source terms of the integral equation. Our method treats the singular terms in the data associated with the delta function to arbitrarily high order, which allows us to construct a quickly-convergent numerical scheme for the solution of the problem. We give several numerical examples illustrating the convergence rates achieved in the solution and the improvements offered by our algorithm over classical approaches.