I will actually go ahead and say that clean water is all you need.
Fish can heal on their own, they don't need that much help usually unless it looks like there is a problem. Calm down and don't get too upset. Cuts happen in fish, just like in other critters. Generally, a fish's immune system will heal it up just fine so long as the water is kept clean. I have actually never used either salt or melafix to treat a wound. My fish have done fine without it. Melafix is a VERY mild med that is rarely worth it's price IMO.
Please do NOT add any chemicals or salt to the tank yet. First, can you please tell us what else is in the tank and a bit about your set-up? Salt is indeed often a good way to go if there is an infection or something, but no need to complicate things if you don't have to. Also, not all fish and plants react well to salt. That is why I am asking about what else is your tank before recommending salt.
Also, are you certain that is it a cut and not a different sort if issue? Do you see any white spots, fuzziness, or anything else odd like that?