When my goslings and ducklings were that age, I used a bowl and overturned another bowl inside it that was slightly smaller in diameter. They had enough water to dip their beaks in, and rinse, but not enough to get really wet in, although they tried they couldn't climb over the bowl in the center. . . I had more troubles with the ducks actually. As they go taller I found buckets in increasing sizes so they couldn't climb into them, but could still get their heads washed . . . and I think I did use a chick waterer -- the plastic ones with the red rim, not the glass jar kind. Until their beaks/heads get too large to fit in the slot, they were able to rinse pretty well in there.
Someone in the duck section has a great brooder waterer design -- very mess free . . .
I didn't let mine go swimming in a kiddie pond till they were all feathered out - which was absurdly early compared with chicks -- maybe at the 6 to 8 wk mark. But I think if you brought them inside the house or made sure they dried completely that it might be okay for just a few minutes, especially if it was warm.