You can leave him there for up to ten days.
BUT. This is exactly how my fish Sid's columnaris started. The fuzzies actually fell off like that with or without salt.. they came and went and came and went.. I was convinced he was cured for a few weeks, then they came back badly, he got super aggressive fin rot overnight and went downhill from there.
Not saying this -will- happen to your fish.. but if his fins start fraying badly after this salt treatment, get him medication for columnaris. It doesn't always show as white fuzz on skin or fins. In Sid's case it became fin rot that wouldn't cure and then cottonmouth disease. He was sickly when I got him, though.. if your betta is healthy to begin with, he might not progress to that state.
The thing about that disease is that it thrives in high temps... so keeping the temp above 74 or so is encouraging it to grow.. (sorry, I see you do have cooler temps - this is a good thing right now.. when he recovers fully and stays healthy, think about getting him a bigger tank & heater.. being cold = lower immune system.. )
Not trying to panic you - just see how he goes, he will probably be okay. But to be safe, do some research on columnaris treatment and perhaps make sure you can get the right medication for it easily, if your fish has a/ any recurrence of these fuzzies after the salt treatment or b/ sudden, hard to shift fin rot, mouth hanging open all the time like something's stuck in, white fuzz on his head or body.
It's an aggressive condition and treatment needs to be prompt to work, so it's best to be prepared. I learned that the hard way. :\
ETA: It isn't slime coat if it's taking portions of fin off with it...