You're essentially asking for medical advice online. Use common sense and be critical of what you read.
Always follow your pediatrician's advice rather than what you read online. If you feel you're not confident with his advice, ask another pediatrician.
Having said that, here's what we were told (in 2009):
The stump will dry out and fall off within a few days. Keep it clean (using water and if necessary cotton swabs), and keep it dry (using cosmetic pads to gently wipe the surrounding area, then put baby powder on the stump. No oils or alcohols are needed (but you might have received different advice!).
You're probably right that alcohol dries it faster, but I don't see a reason for doing that. Let nature do it's thing; it's not dangerous and the child has no nerves there so it can't hurt him in any way.