Can a Hidden Windsinger return a unit to hand on another battlefield?

No, you cannot.

When you play a unit from "Hidden," the targeting choices for its play effect are restricted to the battlefield where the card was hidden (Rule 811.1.d.2).

While Windsinger has an effect that allows you to return a unit to its owner's hand, because you are playing it from a hidden state, that target must be at the same battlefield where the Windsinger was hidden. It cannot target units at a different battlefield.