CuCl is white. CuCl2 is green. CuCl slowly oxidizes to CuCl2, which causes the green color. If the object is ancient, it should be mostly CuCl2. Sulfuric acid will react with CuCl2 but not with Cu.
H2SO4 + CuCl2 --> 2HCl + CuSO4
CuSO4 is blue and souble in water. The HCl will be given off as a gas. Watch out though, HCl is poisonous by inhalation and CuSO4 is poisonous when ingested.