Word for the superclass of buttons, zippers, and pegs?
I suggest fastening (“a hook or similar restraint used to fasten things together”). By the way, if you were referring to snaps, catches, etc. as used with jewelry, the proper word probably would be finding (“A self-contained component of assembled jewellery”). By extension, snaps and hooks used with clothing might also be called findings.
When confined to clothing, clothing fasteners seems to be the perfect general term to me. (But keep in mind I am not a native English speaker.)