We study chaotic scattering outside the wide band limit, as the Fermi energy $E_F$ approaches the band edges $E_B$ of a one-dimensional lattice embedding a scattering region of $M$ sites. The Hamiltonian $H_M$ of this region is taken from the Cauchy orthogonal ensemble. The scattering is chaotic at $E_F$ if the average level density per site of $H_M$ at $E_F$ describes a semi-circle as $E_F$ varies inside the conduction band. The edges of this semi-circle coincide with the band edges $E_B$. We show that the delay-time and thermopower distributions differ near the edges from the universal expressions valid in the bulk. To obtain the asymptotic universal forms of these edge distributions, one must keep constant the energy distance $E_F-E_B$ measured in unit of the same energy scale $\propto M^{-1/3}$ which is used for rescaling the energy level spacings at the spectrum edges of large Gaussian matrices. In particular the delay-time and the thermopower have the same universal edge distributions for arbitrary $M$ as those for an $M=2$ scatterer, which we obtain analytically.