I know it sounds counter intuitive, but the best thing to do, is to just let them go into the hole once they're on their way. Most sink drains have a "U" curve in them. The snake usually won't go any farther than that. If you fill the sink up and cold water starts trickling in through the overflow drain, the snake will usually make a hasty exit back out. The curve causes the drain to flood at that point. (the water won't flush the snake down if it's just a trickle) The snake's instinct, to avoid drowning, is to go against the water coming in. In other words, back out of the hole he came in. I've never had that fail.
Better yet, don't let it happen ever again. The snake probably wasn't seriously injured. I wouldn't worry too much.
From now on, I'll treat others like they treat me. Some will be glad, others should be scared