That is not how copyright works. Music in the US and many similar legal systems has a compulsory license provision that allows for anyone to produce and distribute covers of music as long as all licensing requirements are met. With the long history of covers in music, how much enforcement there is around the meeting the licensing requirements bit varies pretty wildly. If you are not complying with the licensing terms, however, and the rights holder comes after you, no amount of having copied the song by hand will protect you from copyright claims.

Similarly, I can't draw a batman cartoon with pencil and paper and avoid copyright claims when I try to sell the episodes.

Please do not go around infringing on copyright and thinking it's OK because you recreated whatever it was by hand.