The semimetallic behavior of the so-called ``failed Kondo insulator'' CeNiSn has been ascribed to a nodal line in the Kondo hybridization derived from a particular symmetry of the Ce $4f$ orbitals ground state. Here we investigate the geometry of the CeNiSn conduction band by combined angle-resolved photoemission spectroscopy (ARPES) in the high-temperature regime and Open core generalized gradient approximation plus spin-orbit coupling calculations, in order to determine how the nodal hybridization takes place. We identify the Fermi sheet involved in the semimetallic regime from its locus and its shape, respectively, in agreement with the expected nodal line and with quantum oscillations. We further extrapolate and discuss the low-temperature Fermi surface in terms of the expected nodal hybridization with a localized $f$-level. The obtained hypothetical low-temperature Fermi surface is compatible with the description from quantum oscillations, and with both the highly anisotropic magnetoresistance and the isotropic Nernst effect. This work offers an overview of the conduction band of CeNiSn before hybridization, and it paves the way to a definitive understanding of its low-temperature state. In addition, this work serves as a basis for more challenging low-temperature ARPES measurements.