Antonyms for the phrase "had a swing at" could include words that convey reservation, reluctance or avoidance. "Avoided," "abstained from," "eschewed," or "refrained" could all be used in contrast to the phrase to suggest a more passive or cautious approach. Alternatively, antonyms that indicate a more thoughtful, introspective approach might include "considered," "pondered," or "contemplated," suggesting a more measured or reflective decision-making process. Ultimately, the antonyms will depend on the context in which the phrase is used, and the specific tone or style the writer is attempting to convey.