I would not consider this interaction to involve any redox. It is more like an acid-base reaction. The copper in CuO is in the +2 oxidation state no matter how much water is stick to the surface. The extent of hydration may influence the energy levels of the material and how it interacts with other substances, thereby making it easier to reduce or oxidize, but there is no redox in the formation of the water layer on a metal oxide.
So if you immerse your sample in acid condition (more H+), your sample is protonated,
S-OH + H+ --> S-OH2+, by this condition, your sample charge became positive, you can utilize your CuO as an adsorbent, especially to adsorb negative ion
If you change to base condition, your sample charge became negative, can adsorb any positive ion , maybe heavy metal adsorption like that
But, it depends pH zero point charge of your sample. Please check what is pH-zpc of your sample. (pH-zpc = zero point charge) in some references.
In simply: if you immerse your sample in solution in pH below pH-zpc, then your sample is protonated and vice versa.