If memory serves me correctly, drivers in Greece are required to carry their driving licences with them (the same rule applying to tourists). If you don't have your licence, I suspect you may be guilty of an offence, which may cause problems if you are stopped by the police. On this basis, it probably isn't woth while taking the chance (unless you want Mike off your hands for a while! LOL).
Driving in Corfu isn't that bad, provided you take your time and concentrate at all times - try not to get distracted from the views. Take care at the blind bends on mountain roads and look out for the mirrors which will show you if anything is coming the other way. Also, let local traffic overtake when you can - you may have all the time in the world as you are on holiday, but locals are working and may be busy.
Due to my current incapacity, Lynn drove us when out in Corfu in August (I ahve always done all of the driving)ans even she says it isn't too bad.