There isn't exactly one moment of collision like snooker balls, the two spiral and merge and then settle down to look like one bigger black hole. But the time during which most of the energy is radiated is quite short, like 0.1s.
The missing mass is precisely the amount of energy that was radiated away.
We should not think of the mass of the black hole as being the amount of matter stored inside, which may escape... regardless of how it was created, the black hole is just a ball of pure gravity. Its mass is defined by its effect on things far away. You can measure the mass of Jupiter by watching how fast a satellite orbits, and a black hole whose satellites had the same orbits would be said to have the same mass.
