There were no explicitly outlined contingency plans that I have ever seen. The Little Boy bomb was expected to have a nuclear yield no matter what happened, because of its simple design. The Fat Man bomb had contact fuzes on the nose that would cause it to scuttle if it failed to detonate correctly, dispersing the fissile material in an unrecoverable way. They probably would have followed up such a botched raid with an incendiary raid just to make sure. In both cases, the kinetic energy from colliding with the ground would have damaged the bombs practically beyond all recognition (as was the case even when they were just drop-testing ballistic casings at Wendover field, which weren't loaded with explosives). Keep in mind that the Fat Man bomb contained about as much conventional high explosive as the Oklahoma City bomb, so even without a nuclear yield it would be a pretty big bang. The Little Boy bomb contained a lot less (just some cordite bags) but it had a tremendous amount of fissile material in it.

As for reverse engineering the bomb, I don't see it really being possible unless they somehow had a complete, un-damaged prototype. I can think of no plausible situation in which they would have gotten their hands on something like that. The operation of the Little Boy bomb was simple and would have been easy for a scientist to diagnose. The Fat Man bomb was much more technically and conceptually complicated and would have required careful dissection and analysis if they didn't know what they were looking at. Keep in mind that nuclear weapons were theoretically possible were known by scientists all over the world at that point.

The hardest part in manufacturing a nuclear bomb isn't the engineering, it is obtaining the fuel, either U-235 or plutonium. For example, currently Iran knows exactly how to build an atomic bomb, it is just incredibly expensive and time consuming to create the fuel even in 2014 peacetime conditions. 1945 Japan suffering under a blockade and a bombing campaign would never have been able to manufacture either U-235 or plutonium.

The engineering of the Fat Man (plutonium bomb) is much more advanced than that of the Little Boy (uranium bomb). It is safe to say that Japan would not have been capable of developing the shaped charges for a Fat Man type bomb necessary to perfectly collapse a sphere of plutonium. The creation of those shaped charges is probably the pinnacle of mankind's pre-computer calculations (well technically there was some computer help but it was minimal). The engineering of the gun type Little Boy bomb is much simpler, in laymans terms you shoot two pieces of uranium together making them super dense to induce critciallity. 1945 Japan probably could technically manufacture this bomb (over the course of months to years if they were totally devoted) but then there is still the issue of manufacturing the U-235.

And even if Japan did develop a bomb they had no airplane capable of delivering it. The payload exceeded the capability of all of their planes.

So there was no need for a contingency plan since there was 0% possibility of them creating a bomb from a failed detonation.