Black hole (BH) shadows in dynamical binary BHs have been produced via ray-tracing techniques on top of computationally expensive fully non-linear numerical relativity simulations.
On arXiv:1805.03798 [gr-qc], it is illustrated (as a proof of concept) that the main features of these shadows can be captured by a simple quasi-static evolution of the photon orbits on top of a static double-Schwarzschild family of solutions, which is exact.
Whilst the latter contains a conical singularity between the line separating the two BHs, this produces no major observable effect on the shadows.
The following videos illustrate this quasi-static approximation:
link video 1 --> colored background;
link video 2 ---> Milky Way sky background, by the European Southern Observatory (ESO).