I have played it on electric and acoustic, and my memory fails me to remember the differences.
Generally during the first recordings also on electric when playing much louder I always hear a lot of string vibration/noise due to accidental touch, letting go of the string too hard, etc. 
But I can imagine that on an acoustic the hum is worse, the string vibrates more easily, I think (
I really have to pay close attention ) I usually have my use fingertips of free fingers from pickinghand with vingerstyle and use my thumb on the side of the upper strings. My further knowledge ends here because I will eventually try something. Maybe someone will come up with the solution(s), but anyway… practice practice and it will work out fine by itself 
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Greetings 
Edit:
Muting with Fingerstyle?
Here is some information about it I hope in unanswered questions I saw this, and perhaps Richard, who later says that the answers have been added…maybe 