Can I wash my baby’s hands for Negel Vaaser over dishes in the kitchen sink?

Negel Vaaser shouldn’t be washed over dishes unless one is certain they will be rinsed afterwards.

ראה הליכות שלמה תפלה כ הע׳ יא. אשי ישראל ב הע׳ עב.

See here and here regarding washing kids hands.