It looks fun, but I fear that voltage in water will produce H+ and OH- that poison your field-sensitive molecules. Also, water will reduce the electrostatic force exerted on the flexible molecule, down to zero if water is the more polar species.
Maybe you could just attract the droplet electrostatically. I'd use AC field through an insulator. Just water's permittivity would let attract it. Long ago I used XY plotters that held the paper sheet with two interleaved electrodes and an electric field, this was very effective. It may need water pure enough to limit heating, and a frequency high enough: for a given purity, compare the conductivity with the capacitance hence susceptance.
You could try with a printed circuit, the epoxy against water, the printed electrodes dry. Just spray some teflon, or glue a teflon film, to remove unprovoked wetting.
Or try to vibrate the substrate with piezo actuators where the droplet shall not stay.