I've read that one's stale moves is tracked by the move-performer rather than who (or what) has been hit. Do attacks that hit stuff like Yoshi's Story's Fly Guys or Peach's turnips enter the stale move queue?
Since you're asking for Melee, here's the answer: No. Stage elements, items, and shields do not cause attacks to stale when hit (and therefore also do not refresh other moves). In addition, moves that hit multiple opponents at once only stale by one level.