Lyman-$\alpha$ (Ly$\alpha$) spectra provide insights into the small-scale structure and kinematics of neutral hydrogen (HI) within galaxies as well as the ionization state of the intergalactic medium (IGM). The former defines the intrinsic spectrum of a galaxy, which is modified by the latter. These two effects are degenerate. Using the IllustrisTNG100 simulation, we study the impact of the IGM on Ly$\alpha$ spectral shapes between $z\sim 0$ and $5$. We compute the distribution of the expected Ly$\alpha$ peaks and of the peak asymmetry for different intrinsic spectra, redshifts and large-scale environments. We find that the commonly used \textit{averaged} transmission curves give an incorrect perception of the observed spectral properties. We show that the distributions of peak counts and asymmetry can lift the degeneracy between the intrinsic spectrum and the IGM absorption. For example, we expect a significant number of triple peaked Ly$\alpha$ spectra (up to 30% at $z\sim 3$) if the galaxies’ HI distribution become more porous at higher redshift as predicted by cosmological simulations. We provide a public catalog of transmission curves to be used in future simulations and observations to allow a more realistic IGM treatment.