The liquid in the NiCd cells is a pure potassium hydroxide and water. Neither Nickel nor Cadmium are dissolved in it in detectable amounts.
It is corrosive and it also can burn the skin (or eyes!), but not particularly poisonous.
Exposed to air, potassium hydroxide converts to potassium carbonate - it is somewhat less corrosive and generally not dangerous (but be careful anyway).
The substance that one can use to wash it away is the pure water. Distilled water is overkill, any drink-safe water is OK. Most printed circuit board materials survive short (few hours) exposition to water pretty well and the pure water cannot do more damage than the cell electrolyte already did anyway.
Soaking the board in water for an hour or two and/or using a brush are allowed approaches.
Be sure to dry the PCB very well (beware of water between the board and the elements) before energizing it.
Compressed air can be used for best results against the hidden droplets.
Washing it with ethanol (after the water) can accelerate drying pretty well, but ethanol can wash some paint from the PCB or the components and this is probably not what you want with a single item.
Quite often a well-cleaned PCB starts working "like new". Try this before any other attempts.