Short answer - The real word risk is probably small on a knife that is taken care of.
Big Blues' knife will not automatically start to corrode unless it gets wet and is left to corrode. It would rust under the same conditions without the copper.
Copper and iron are galvanicly well separated. The more the separation, the worse the corrosion problem due to galvanic action. Other metal combinations are less active. The situation is also acerbated by the fact that both metals will oxidize easily all by themselves. Add low Ph water and some electrolytes, and it can get nasty.
Vaunripped asked about silver solder...and he is right to consider this where there will be continues exposure to electrolytes. The Thresher submarine disaster was possibly caused by the silver solder joints failing due to galvanic corrosion. Under the conditions a knife will be used, it is not a concern.
The physics of it is that the metals should be less than .25-.50V apart in galvanic potential. The more harsh the electrolytic conditions ( like saltwater), the closer they need to be. Nickel, copper, brass,bronze ( common knife hardware materials) all have a galvanic index (GI) about .30-.40V. Steel is about GI .89-.90V. Thus these items would corrode by galvanic action if left wet or in water. Copper, Brass, and nickel however will last almost forever when used together, which is why they work so good in sculpture and statuary.
Some of us are old enough to remember making a battery from a pennies and dimes,spaced with blotter paper , and soaked with salt water ( back when pennies were copper and dimes were silver). The potential difference is only .20V between these metals, so one penny/dime unit ( a cell) will only make a .20v current. But when we make a stack with eight of each ( a battery) then we get 1.5V ( there is some loss due to resistance).
A near perfect battery would be gold and beryllium, but zinc and carbon are far cheaper and more plentiful.