Does anyone have any experience with this stuff?

We go to a Halloween/trick or treating party with multiple friends every year, and this year I've decided to make Witch's Brew to take. I know to use tongs, of course....Do you just drop the chunk of dry ice in the punch? Or break it up first? Will it all dissolve in a few hours? If not, how do you dispose of it? I have stainless steel sinks, would it harm that?