More simply, starting with Cl2 + NaOH implies:
Cl2 + NaOH = NaCl + NaOCl
with the above reaction being the basis for the commercial production of aqueous chlorine bleach.
So, equivalently, we should be able to start with commercial bleach (which is actually not pure NaOCl, but sodium hypochlorite plus NaCl).
Interestingly, if there is an electrochemical ...