Charge transfer (or exchange) reactions between hydrogen atoms and protons in collisionless shocks of supernova remnants (SNRs) are a natural way of producing broad Balmer, Lyman, and other lines of hydrogen. We wish to quantify the importance of shock-induced, non-thermal hydrogen emission from SNRs in young galaxies. We present a method estimating the luminosity of broad (∼1000km/s) Lyα, Lyβ, Lyγ, Hβ and Pα lines, as well as the broad and narrow luminosities of the two-photon (2γ) continuum, from existing measurements of the Hα flux. We consider cases of β=0.1 and 1, where β=Te
is the ratio of electron-to-proton temperatures. We examine a modest sample of 8 proximate, Balmer-dominated SNRs from our Galaxy and the Large Magellanic Cloud. The expected broad Lyα luminosity per object is at most ∼1036
erg/s. The 2γ continuum luminosities are comparable to the broad Hα and Lyα ones. We restrict our analysis to homogenous and static media. Differences in the Lyα/Hα and Lyβ/Hα luminosity ratios between the β=0.1 and 1 cases are factors ∼2 for shock velocities 1000≲vs
≲4000km/s, thereby providing a direct and unique way to measure β. In principle, broad, ``non-radiative'' Lyα from SNRs in young galaxies can be directly observed in the optical range of wavelengths. However, by taking the different rates between core collapse and thermonuclear supernovae into consideration, as well as the duration we expect to observe such Lyα emission from SNRs, we expect their contribution to the total Lyα luminosity from z∼3 to 5 galaxies to be negligibly small (∼0.001%), compared to the radiative shock mechanism described by Shull & Silk (1979ApJ...234..427S
). Although broad, non-thermal Lyα emission has never been observed, these photons are produced in SNRs. Hence, the non-radiative Lyα luminosity is a part of the intrinsic Lyα spectrum of young galaxies.