To clear up the air a bit here about the copper use:
The oxide of copper that you *might* very slightly be concerned about is the common patina you would see anywhere that copper is exposed to the atmosphere we humans live in. It is of very little concern as this same patina is actually a natural protective layer. It is not detrimental to the actual copper metal, unlike that oxide of iron, better known as rust, a.k.a. corrosion. It is the manner in which aluminium protects itself from further corrosion as well. You'll likely end up with a slightly greenish discoloration on the copper surfaces that are exposed to atmosphere...a touch of copper polish will deal with that if you are actually concerned about the cosmetics of the internals of your computer case.
There's a reason copper tubing is preferred for use as the water supply in your home, other than being somewhat flexible and able to deal with temperature variances, and that is for its safety of carrying potable water. For the most part it will also stand up perfectly to any number of different fluids used for active cooling. A car radiator is often times made of copper, copper alloy or aluminium for the same reasons other than excellent heat conduction. Automotive coolant fluids contain some dicey chemicals, but the (copper) alloys used perform perfectly for ages. Coolant fluids used for CPU cooling duties are far more likely to (negatively) affect the polymers used in all the joins, joints and fittings of the liquid cooling system; which is why there's a list of required/recommended fluids to use.
I suspect the Nickel coating is solely for the ooh-shiny-thing appeal, as its capabilities to transfer heat away from the CPU in this setting is no different than Copper. If anything at all, the difference would be negligible at best.
I suppose if you want a bit of a steam-punkish look to the internals of your computer case, then go with copper and accelerate the patina reaction.
