Why not use Cu(OH)2 as a dye for protein electrophoresis?
Copper hydroxide does not dissolve very well in water, which means you will have trouble soaking them into your gels. 

Also, even if you managed to add enough copper hydroxide beforehand (in the wells), it is unlikely that the copper(II) ions, if any existes, will travel along with the protein due to its size. (Copper hydroxide itself does not have any charge.)

As for the paper Stella mentioned, the copper salts are used after electrophoresis to produce a negative image, which is exactly what you cannot do with copper hydroxide.