Betadine (povidone iodine) was used for decades (since 1955, and earlier since the 1800’s with simple iodine) in hospitals all over the world in prepping for surgery, flushing out surgical incisions, in handwashing, and treatment of wounds. It is useful to treat newborn’s eyes to help prevent...
The cat nail clippers might work, but dog nail clippers can work on chickens. You just want to clip off the point of the spurs and make it more dull. Some Tractor Supply stores have Fish Mox on the shelves, but it varies. Call ahead and ask.
You can trim the sharp tip with a dog nail clipper or a file. Is there a place to keep him separated outside, in a garage or a basement? I would bring him inside at least for the soaking unless you are somewhere very warm right now. Where are you located?
This looks like he might have had a leg band that got too tight and possibly caused some swelling. He may have pecked at it himself or had it injured by another chicken or rooster. What you are doing with cleaning it is good. I would probably soak his lega in warm soapy water daily for about 20...