Sound of ropes / strings / clothing material sliding against each other?

Solution 1:

Even though an actual zipper isn't involved, the sound of sharp humming associated with movement can be onomatopoeically described by zipping:

"He doesn't feel like he is finally home for the night until he listens to the zip, zip of pulling his shoelace knots undone while sitting at the edge of the living room sofa."

Since zippers are sometimes found in footwear, however, to avoid confusion, you might want to go full onomatopoeic:

"He doesn't feel like he is finally home for the night until he listens to the sszp, sszp of pulling his shoelace knots undone while sitting at the edge of the living room sofa."

I pulled this spelling out of the air; customize as desired.

(Note that the sound that ropes make under load is often described as "squeaking", but your example sentence precludes this use, as the shoelaces are no longer tight.)

Solution 2:

Fabric whispers. It frequently rustles (particularly skirts)--a description that doesn't necessarily imply the crackling aspect that it entails for leaves/paper.

Shoelaces would probably also whisper. I might describe the sound in the clip as a hiss, but I think that comes off a little too sinister as a description for the example of "feeling at home."