No need to dose with anything at this stage, it is a minor injury, clean water will do the trick. That white part you see will pretty much just fall off.
That is a typical injury that would be sustained by having his/her tail pecked at by a tankmate. Usually the tip that cops it. No real harm, but tails don't grow back. Losing it bit by bit sucks.
In an evolutionary sense I have always found it odd. Stingrays have such an amazing ability at regenerating - look at the damage females can sustain during mating, and the disk heals back perfectly in all but the absolute most severe cases. But the tail doesn't grow back at all. Which is odd and it is the stingrays main defense.
My take on dosing and adding things like salt for stingray injuries is pretty simple - stingrays are tough SOB's. If your water is clean and the animal is healthy - it is very seldom needed. Adding medications or even salt is just one more way a keeper can mess things up. To put it into perspective one of my females has been stabbed near the gills (noticed it this morning) - this is the second time that has happened in the last 12 months. I'd forgotten about it until I read this thread - it will heal fine without me doing anything extra.