We study the exciton contribution to the third-order optical susceptibility of one-dimensional semiconductor quantum dots and show that the screening of the electron-hole interaction has a strong influence on the nonlinear optical properties in the weak confinement regime. Based on a density matrix formulation, we estimate the spectrum of the third-order optical susceptibility and its contribution to the refraction index and absorption coefficient. In particular, we show that the multipeaked spectrum of the nonlinear susceptibility, which results from the hydrogenoid character of the exciton eigenstates for a purely Coulombian electron-hole coupling, is reverted towards a single peaked structure as the interaction becomes strongly screened, thus leading to a substantial enhancement of the nonlinear optical properties of semiconductor quantum dots.