I strongly suggest yes, unless you can clearly demonstrate that the voltage was such that no significant injury is possible. Incidents should be recorded and investigated on the basis of 'what are the reasonable worst case consequences?', not on what actually did happen (otherwise what's the point of encouraging 'near miss' reporting?

Yes. An electric shock has the potential to cause injury or damage, so at the least should be recorded as an incident. It would also be worth recommending he report it to his boss as they should have a record of it too.

There is no doubt that there was an incident, but I am not sure that there was "injury". The statutory "Accident Book" is meant for "injuries". What was the impact of the electic shock on the individual? Was a first-aider etc involved? The deatils regarding this will also contribute to making a judgement. I presume that in addition to the "Accident Book", you have your internal system of reporting & recording of non-injury incidents/near misses etc.