Two nearby B-type stars, $\epsilon$ CMa ($124\pm2$ pc) and $\beta$ CMa ($151\pm5$ pc), are important contributors to the photoionization of the local interstellar clouds. At spectral type B1 II-III, $\beta$ CMa is slightly hotter than $\epsilon$ CMa (B2 II-III), but its ionizing flux at Earth is attenuated by a much larger H I column density. At the external surface of the clouds, the two stars produce similar fluxes in the Lyman continuum (LyC). From the $\beta$ CMa angular diameter, bolometric flux, and position on the Hertzsprung-Russell diagram, we obtain a consistent set of stellar parameters: $T_{\rm eff} = 25,180\pm1120$ K, $\log g = 3.70\pm0.08$, radius $R = 8.44\pm0.56\,R_{\odot}$, mass $M = 13\pm1\,M_{\odot}$, and luminosity $L = 10^{4.41\pm0.06}\, L_{\odot}$. The EUVE-observed fluxes and non-LTE model atmospheres are used to determine the ionizing photon production rate $Q_{\rm H} = 10^{46.0}$ photons s$^{-1}$ and fluxes incident on the local clouds, $\Phi_{\rm HI} \approx 3700$ cm$^{-2}$ s$^{-1}$ and $\Phi_{\rm HeI} \approx 110$ cm$^{-2}$ s$^{-1}$ in the H I and He I continua. The corresponding photoionization rates are $\Gamma_{\rm HI} \approx 1.5\times10^{-14}$ s$^{-1}$ and $\Gamma_{\rm HeI} \approx 7.3\times10^{-16}$ s$^{-1}$. Within the local cloud, the LyC flux is attenuated by an H I column density $N_{\rm HI} = (1.9\pm0.1)\times10^{18}$ cm$^{-2}$, with optical depth $\tau_{\rm LL} = 12.0\pm 0.6$ at the Lyman limit. The radial velocities and proper motions of $\beta$ CMa and $\epsilon$ CMa indicate that both stars passed within $10\pm1$ pc of the Sun approximately 4.4 Myr ago, with incident ionizing fluxes 180-200 times larger. Their EUV radiation photoionized and heated the tunnel in the local interstellar gas, associated dynamically with past supernova explosions in the Sco-Cen OB association.