The Ultra-Violet Italian Sky Surveyor (UVISS) is a small SiC far-and near-UV telescope under study by the Italian Space Agency to be installed on an available Express Pallet (ExPa) of the International Space Station (ISS). UVISS has two focal plane instruments: an ultraviolet imaging camera and a far ultraviolet spectrograph. This paper summarizes the conclusions of the study about the optical configuration of the spectrograph. This instrument has to cover the 91-130 nm spectral region with a moderately low resolving power (greater than 300 at 100 nm), a spatial resolution of 4 arcsec on-axis and minimization of spatial aberrations over arcmin's long entrance slit. Many problems had to be faced in the design of this instrument: from the very small available room, to the rather short visibility time of a single target on the sky, to the intrinsic pointing instability of the ISS. The adopted configuration of the spectrograph foresees the use of a spherical grating with parallel variable line spacing in the Harada mounting. The theoretical performance of this instrument obtained by ray-tracing simulation is given, showing that the optical requirements can be satisfied. Also, several efforts have been done in order to study the possibility of reconstructing the target spectra by means of a photon recentering technique to compensate the pointing instabilities due to the ISS environment. The details of this analysis are described, showing that the system optical performance can essentially be maintained also with a carrier so unstable as the ISS.