My experience is in electronics, not chemistry, so take my advice as you will… Distilled or RO that hasn’t been remineralized would be your cleanest bet yes, and you would need an electrolyte. To my knowledge you want a positively ionizing electrolyte, table salt comes to mind. That’s where I’m unsure how your copper cathode would fair, it makes sense it should be ok, but I don’t know. If it were me I’d keep the number of materials in the solution to a minimum to reduce possibility of contamination.
As to a reducing agent… no help for you there, sorry. The process of electrolysis should create the colloid though, so I am not sure what the benefit would be. But admittedly all the information I could gather on it is largely holistic medicine nonsense.