Will oxidation/reduction of copper still occur in an electrochemical cell if it is not in an aqueous environment?
It is certainly possible for metals, including copper, to corrode in non-aqueous environments.  The details depend on the precise nature of the solvent, electrolytes, and other potentially complexing species present.  For example, in polar protic solvents (like water) that don't have any complexing ligands for copper, the equilibrium potential for copper oxidation will likely be the same as in water.  But oxidation potentials will likely shift in solvents that are non-polar, in ways that depend strongly on the composition of the electrolyte.

However, if you are using potassium hydroxide as the electrolyte, your conditions might be more aqueous than you think.  You can think of "hydroxide" as a type of water that likes to exist at high pHs.  And hydroxide itself generates high pHs.

Elecrochemical water oxidation occurs via this reaction:

$$\ce{2 H2O -&gt; O2 + 4 H+ + 4e-}$$

The pH-dependent equilibrium potential is $1.23~\rm{V} - 0.059\frac{\rm V}{pH}\times pH $, which at a pH of 14 comes out to 0.4 volts.  So you might also possibly be irreversibly oxidizing hydroxide to oxygen during your electrolysis.