The extensive use of social networks has led to significant privacy concerns, as users frequently share sensitive information that can be exploited. This study investigates the ability of lightweight, open-source, and locally executable linguistic models to effectively recognize potential privacy risks in social network posts. We evaluate eight models from the LLaMA, Gemma and Qwen families using a zero-shot approach on a Spanish tweet dataset. Our evaluation demonstrates that lightweight LLMs are able to perform the qualification of potential privacy risks acceptably. However, the results also reveal substantial variability, as the models have significant difficulties in detecting subtle or less frequent categories, such as personal attacks or identifiable information, and often obtain low F1 scores despite their high accuracy. These results highlight the potential of accessible LLMs for privacy protection tools, but underscore the need for improved detection performance on sensitive data types to enable robust and reliable applications.