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Black hole (BH) shadows in dynamical binary BHs (BBHs) have been produced via ray-tracing techniques on top of expensive fully nonlinear numerical relativity simulations. We show that the main features of these shadows are captured by a simple quasistatic resolution of the photon orbits on top of the static double-Schwarzschild family of solutions. While the latter contains a conical singularity between the line separating the two BHs, this produces no major observable effect on the shadows, by virtue of the underlying cylindrical symmetry of the problem. This symmetry is also present in the stationary BBH solution comprising two Kerr BHs separated by a massless strut. We produce images of the shadows of the exact stationary corotating (even) and counterrotating (odd) stationary BBH configurations. This allows us to assess the impact on the binary shadows of the intrinsic spin of the BHs, contrasting it with the effect of the orbital angular momentum. [ABSTRACT FROM AUTHOR]