A sample of quasars has been recently assembled to investigate the non-linear relation between their monochromatic luminosities at 2500{AA}, and 2keV and to exploit quasars as a new class of 'standardized candles'. The use of this technique for cosmological purposes relies on the non-evolution with redshift of the UV-optical spectral properties of quasars, as well as on the absence of possible contaminants such as dust extinction and host galaxy contribution. We address these possible issues by analysing the spectral properties of our cosmological quasar sample. We produced composite spectra in different bins of redshift and accretion parameters (black hole mass, bolometric luminosity), to investigate any possible evolution of the spectral properties of the continuum of the composites with these parameters. We found a remarkable similarity amongst the various stacked spectra. Apart from the well known evolution of the emission lines with luminosity (i.e. the Baldwin effect) and black hole mass (i.e. the virial relation), the overall shape of the continuum, produced by the accretion disc, does not show any statistically significant trend with black-hole mass (M_BH_), bolometric luminosity (L_bol_), or redshift (z). The composite spectrum of our quasar sample is consistent with negligible levels of both intrinsic reddening (with a colour excess E(B-V)<~0.01) and host galaxy emission (less than 10%) in the optical. We tested whether unaccounted dust extinction could explain the discrepancy between our cosmographic fit of the Hubble-Lemaitre diagram and the concordance {LAMBDA}CDM model. The average colour excess required to solve the tension should increase with redshift up to unphysically high values (E(B-V)~=0.1 at z>3) that would imply that the intrinsic emission of quasars is much bluer and more luminous than ever reported in observed spectra. The similarity of quasar spectra across the parameter space excludes a significant evolution of the average continuum properties with any of the explored parameters, confirming the reliability of our sample for cosmological applications. Lastly, dust reddening cannot account for the observed tension between the Hubble--Lemaitre diagram of quasars and the {LAMBDA}CDM model.