Forbidden nonunique β decays feature shape functions that are complicated combinations of different nuclear matrix elements and phase-space factors. Furthermore, they depend in a very nontrivial way on the values of the weak coupling constants, gV for the vector part and gA for the axial-vector part. In this work we include also the usually omitted second-order terms in the shape functions to see their effect on the computed decay half-lives and electron spectra (β spectra). As examples we study the fourth-forbidden nonunique ground-state-to-ground-state β− decay branches of 113Cd and 115In using the microscopic quasiparticle-phonon model and the nuclear shell model. A striking new feature that is reported in this paper is that the calculated shape of the β spectrum is quite sensitive to the values of gV and gA and hence comparison of the calculated with the measured spectrum shape opens a way to determine the values of these coupling constants. This article is designed to show the power of this comparison, coined spectrum-shape method (SSM), by studying the two exemplary β transitions within two different nuclear-structure frameworks. While the SSM seems to confine the gV values close to the canonical value gV = 1.0, the values of gA extracted from the half-life data and by the SSM emerge contradictory in the present calculations. This calls for improved nuclear-structure calculations and more measured data to systematically employ SSM for determination of the effective value of gA in the future.