No need to separate, but might treat the other birds too.
Scaly leg mites can spread but do so pretty slowly.
Treat every few days or at least once a week.
Try to get some of that 'dirt' off....get the oil up under the scales.
I use bag balm, messy but you can pack it up under the raised scales then wipe off as much excess as possible.
I treat my birds off the roost at night, easier to catch that way..haha.
I wear a headlight so I can have both hands free and have a chair in the coop shed so I can sit down with bird on it's back on my lap. Covering their heads with a towel can help calm them down. Always keep their wings contained...the less they are able to struggle the sooner they will submit...and the more you handle them the less most will struggle as they get used to it...talk softly and be calm yourself, they can 'feel' your anxiety.
It will take quite awhile for improvement to show, maybe a little within the first week but can be much longer for new scales to grow in smooth.