Pinocchio
I have hired cars in Corfu for 18years and driven all over the island. In all those times I don't recall a single experience when my wife (the passenger) was obviously nervous about any off-road drops. In my opinion the description of driving there given by Tosca100 is rather exaggerated so don't let it put you off.
You don't say which Agios Stefanos so I can't recommend routes but if it is the north-west one near Arillas you have huge scope for some lovely drives through great scenery in safety. I know a few spectacular 'viewing places' and all have barriers.
The web-site
http://www.agiosgeorgios.info has some suggestions for car trips near Agios Stefanos and if you email me from that web-site I can describe some more.
Obviously the tight bends of the twisty and often pot-holed country lanes call for much slower driving than you are used to in UK.
I suggest you hire a small car with an engine of about 1100 or 1200c.c (not less) which gives you necessary power on the sudden hills but is easy to park or pull over when meeting other vehicles. Many of these narrow lanes in the hills and valleys do have unprotected edges such as in the olive groves where the car could leave the road down a bank if you are careless, drunk or not concentrating. But if you can stay on the road in UK you should be able to stay on the road in Corfu! You don't need to crawl along but do slow down before blind corners and move out well onto your side of the road. If the scenery is particular good then pull over and stop. My wife and I are senior citizens but love driving in Corfu apart from the towns and the few busy main roads. A hire car will add another dimension to your holiday and enable you to see the 'real Corfu'.
Enjoy!!