If you're going to go for something abrasive, sugar is probably milder than salt. Maybe a sugar+oil combo, so your skin gets moisturized at the same time and not as raw?
As for the doctor's appointment, they see all sorts of oddities of the human condition. In my experience they're pretty unflappable. Blue-tinted skin is probably fairly mild on the human foibles spectrum...
Good luck with the remedies.
