Ha, yeah, I would think that the DM and the player could riff together to come up with how to handle the role-play aspects.
A character with charisma of 1 wouldn't just be unattractive or inarticulate. They would be, as [MENTION=80982]pdzoch[/MENTION] puts it, absolutely repulsive. Is that a symptom of something else noticeable, like a terrible stench, or is it more inexplicable? Like, dude looks and sounds normal, but anybody who spends more than 30 seconds with him wants to either punch him in the face or run the hell away. Shopkeepers would refuse him service. People in his company would HOPE that something terrible happens to him so they can pointedly refuse to offer him assistance.
Having a score of 1 in anything is debilitating. Play that to full effect, but make sure that Remove Curse is available soon — I can't imagine it being fun for any more than one session max. Alternatively, have some of the worst effects wear off over time, and have it settle in at a slightly less debilitating Cha of between 3 and 6. Nobody really wants to talk to him or be around him, but if he keeps his head down and his mouth shut, he can spend a day in town without some random stranger "slipping" and pushing him in front of a galloping horse.