If my opponent plays Promising future and from that effect I play Zaun Punk can I wait to see if my opponent plays dazzling aurora to use my zaun punks effect?

Yes — you'll see what your opponent plays before you have to pick a gear, and you can kill their Dazzling Aurora with Zaun Punk's trigger.

Zaun Punk's ability isn't a choice you hold back: if you paid the additional cost (killed a friendly gear), the "when you play me" trigger automatically goes on the chain when he enters play. But because all cards played from Promising Future are finalized in order before pending "when played" triggers finalize (FAQ #7044), your opponent's Dazzling Aurora will already be on the board by the time your trigger finalizes. "Kill a gear" targets are chosen at finalization (Rule 402), so you pick Aurora then and it's killed when the trigger resolves.

One catch: if you didn't kill a friendly gear as the additional cost when you played Zaun Punk, the ability never triggers at all — "if you paid the additional cost" is part of the trigger condition (Rule 383.2.a.1).