  Recent years have witnessed an expanding interest in experimental studies of
$\beta$ electrons (electrons emitted in $\beta^-$ decay transitions) and their
energy distributions, the so-called $\beta$-electron spectra. These experiments
are interested mainly in $\beta$ transitions with electron spectra sensitive to
the effective value of the weak axial coupling $g_{\rm A}$. In the present
paper we make an extensive search for $g_{\rm A}$ sensitive $\beta$ spectral
shapes in the $A=86-99$ region using the nuclear shell model with the well
established Hamiltonians $\textit{glekpn}$ and $\textit{jj45pnb}$, designed to
render a good description of the spectroscopic properties of nuclei in this
mass region. We have found eight $\beta^-$ decay transitions with various
degrees of $g_{\rm A}$ sensitivity. Moreover, these transitions are also
important in pinning down the value of the so-called small relativistic vector
nuclear matrix element, sNME. In addition, some of the corresponding mother
nuclei are important contributors to the antineutrino flux from nuclear
reactors. All this means that the found $\beta$ transitions are potentially of
great interest for future rare-events experiments.
