Non-thermal He II spectra for discharges with helium beam fuelling are analysed. Simulated spectra are used to study the effects of plasma temperature, plasma density and on observed charge-exchange (CX) spectra. Differences in modelling the non-thermal velocity distribution function with a numerical Fokker - Planck code or alternatively using analytical expressions are investigated. The intensities and spectral shapes of both active, localized CX spectra and competing, non-localized, passive electron-impact excitation components are simulated and compared with observations. The `plume' contributions of electron-impact excited particles are found to be quite appreciable and uncertainties in the plume calculation lead to non-negligible errors in the extraction of the active signal from the total spectrum. However, for experimental conditions with magnetic field configurations minimizing the plume effect good agreement can be found between fast-particle densities derived from the numerical calculations and the experimental observations. Significant problems in deriving absolute densities are encountered when a helium beam also acts as a CX diagnostic beam. For the case of dominant passive emission components, simulated fast spectral intensities for the core lines of sight agree within a factor of two with experimental data.