If my opponent plays Fizz to use Hidden Blade targeting my Kayle, can I play Disposable Orders to remove the Hidden Blade from trash before Fizz uses it?

Yes. You can respond to Fizz's "When you play me" trigger with Disposal Order and recycle the targeted Hidden Blade — once it leaves the trash, Fizz's ability has no valid target and its instruction to play the spell is ignored (Rule 359.3.e.7; FAQ #10771).

Timing detail: Fizz's target is declared when his trigger is put on the Chain, so you'll know Hidden Blade is the target before you respond. Since Disposal Order is a Reaction, you may play it while the state is Closed. If you recycle Hidden Blade, it goes to the bottom of your opponent's deck and never gets played — Kayle won't be killed, and no draw 2 for your opponent.