My experience with Kerbal Space Program gives me the impression that it's impossible to transfer from a stable orbit of one body to the stable orbit of another without deceleration. But is this true for a photon? Could light enter a stable orbit of a black hole if fired at the correct angle from a distance?
There are no stable photon orbits around black holes (see this answer).
Black holes do have an unstable photon orbit though. "Unstable" here means that any tiny deviation from this orbit, will case the photon to be either scattered to infinity or sent into the black hole. It should be emphasized that there such orbits are always circular an can exist at only one radius (1.5 times the Schwarzschild radius for a Schwarzschild black hole). There are no elliptic photon orbits. This orbit is often called the "light ring" (or sometimes "photonsphere")
As long as we treat the photon as a perfect massless point (test) particle, we can find a highly fine-tuned trajectory that will asymptote to the light-ring. Of course, in reality, a photon always needs to be a wave packet with a finite size, making this fine tuning impossible in practice.