This is why I went with watering nipples for my chicks. I hung a 1-gallon ice cream pail with two nipples in the brooder and never had any worries about them spilling or fouling their water. You probably don't have enough time left to get the nipples (I had to mail order mine) but the rabbit bottle would be my second choice. The only problem with those is that many of them drip a little and they are designed to clip to a cage so you'd have to figure out a mounting strategy if your brooder has solid walls. Still, better than a nasty waterer full of shavings and droppings or, worse, a tipped waterer because they decide they're big enough now to fly up and roost on it.