Is there a 'when you play me' trigger for shimmering swimmer if I didn't pay the cost?

I can't find a card called "Shimmering Swimmer" — it isn't in my card database, so I can't confirm its printed text or give a ruling on it.

That said, the general rule depends on what "didn't pay the cost" means. A "when you play me" Play Effect triggers from the permanent being played to the board, not from resources changing hands — so if the unit was actually played (even with its cost ignored or reduced to zero), the trigger still goes on the chain (Rule 383.4.a). If instead the card reads like Clockwork Keeper or Sea Monkey ("You may pay [X] as an additional cost to play me. When you play me, if you paid the additional cost, …"), the ability still triggers, but it resolves with no effect because the paid-cost condition fails.

If you can give me the exact printed text or the correct name, I'll rule on the specific card.