Output format selection is a necessary but understudied dimension of few-shot named entity recognition (NER) with large language models. Existing formats carry characteristic failure modes under autoregressive generation, yet output format has not been systematically evaluated as a primary variable in the few-shot setting across diverse domains and entity structural complexity. We evaluate 21 output formats over 17 datasets across two levels of structural entity complexity, using 9 open-weight models without fine-tuning, ranging from 1.7B to 70B parameters. Output format is the main factor affecting performance, with a 41.7 F1 points difference between the best and worst formats. This exceeds the gains from scaling models parameters within-family. Furthermore, output format accounts for approximately 49.1% of F1 variance on simple datasets and 74.9% on complex ones. We describe three mechanistically distinct failure modes that explain these observed differences; each existing format violates at least one of three properties jointly necessary for robust few-shot NER. We propose CANE (Context-Anchored Natural Expression), a format family addressing all three properties. All CANE variants ranked the highest on simple and complex datasets. This includes the GENIA dataset where all other formats had near-zero scores across nine models, indicating the necessity of the three properties. These findings highlight the importance of output format in few-shot named entity recognition, particularly for annotations involving overlapping or discontinuous entities.