We present a new analysis of NuSTAR and Suzaku observations of the black hole Cygnus X-1 in the intermediate state. The analysis is performed using kerrC, a new model for analyzing spectral and spectropolarimetric X-ray observations of black holes. kerrC builds on a large library of simulated black holes in X-ray binaries. The model accounts for the X-ray emission from a geometrically thin, optically thick accretion disk, the propagation of the X-rays through the curved black hole spacetime, the reflection off the accretion disk, and the Comptonization of photons in coronae of different 3D shapes and physical properties before and after the reflection. We present the results from using kerrC for the analysis of archival NuSTAR and Suzaku observations taken on 2015 May 27-28. The best wedge-shaped corona gives a better fit than the cone-shaped corona. Although we included cone-shaped coronae in the funnel regions above and below the black hole to resemble to some degree the common assumption of a compact lamppost corona hovering above and/or below the black hole, the fit chooses a very large version of this corona that makes it possible to Comptonize a sufficiently large fraction of the accretion disk photons to explain the observed power-law emission. The analysis indicates a black hole spin parameter a (-1 ≤ a ≤ 1) between 0.861 and 0.921. The kerrC model provides new insights into the radial distribution of the energy flux of returning and coronal emission irradiating the accretion disk. kerrC furthermore predicts small polarization fractions around 1% in the 2-8 keV energy range of the recently launched Imaging X-ray Polarimetry Explorer. © 2022. The Author(s). Published by the American Astronomical Society.