Meaning there's Sodium chloride (NaCl) in solution which not only makes the solution (more) conductive but also in combination with the application of electric current should electrolyze the solution into gaseous O2, H2 and Cl2.
Would that not be copper oxide?
Source: did that as a teenager and did not die (trying to synthesize hydrogen as any normally constituted teenager would do), and the copper wires just ended up being entirely corroded until the immerged part disappeared. No hydrogen as I did not seal the apparatus properly. But I had a nice blueish precipitate instead. I absolutely had no idea it could have generated chlorine. I did sleep in the same room as the experiment for a full week. So I guess either my bedroom was well ventilated or it did not produce enough chlorine, or that it was just copper oxide.
Even if it did make chlorine, as long as your power wasn't too high it might not hurt you (much) due to ventilation. It is also very reactive, so it tends to get used up reacting with whatever random crap is near it.
Just put the wires at some distance in the salt water and look. The wire emitting the blueish fog (chlorine) is the positive, and the one emitting bubbles (hydrogen) is the negative.