One pickup is all that is needed. The engine uses a "waste spark" ignition. This works because when one cylinder is on compression the other is on exhaust. Most newer cars and Harley engines from the start of V-twins used this method.
The redundancy of the ignition comes from the fact that both coils are fired from both CDI units. Each coil has a spark plug in each cylinder. That way if one CDI dies the engine still runs.
The engine needs a battery for the ignition. This is also for redundancy/safety in an aircraft. If the alternator fails, the battery will supply ignition for time to land safely. You don't say how your going to use this engine, but if for a aircraft, for your own safety and for the safety of people on the ground, the original dual ignition system and battery ignition should be kept.