Why do you think oil would have such and advantage? It is not particularly difficult to design a waterjet using water. Stainless hardware is not ridiculously more expensive than regular steel when building from scratch. I guess for a hobbyist, trying to adapt a hydraulic pump it might make some sense but for industry, no. BTW there are lots of low viscosity organic fluids you could try other than conventional oils. As discussed, flammability is the major issue. I suppose you could go with PCBs but I would not recommend it! I can just imagine aerosolized PCB all over the shop.
Why don't you try using a hydraulic pump to pump water with a corrosion inhibitor? Think water soluble coolant.
Robert