Traditional food products (TFPs) represent a defining part of one’s culture, identity, and heritage with crucial economic, cultural, and environmental benefits in society. Younger generations have a positive idea of TFPs, even if this does not lead to actual purchase, possibly due to the fact that they are often perceived to not meet safety criteria. This study focuses on product communication (CP) and packaging referring to the territory (PT) and to sustainability (SP) in order to verify if these have a direct or mediated impact on perceived product safety (PPS). A structural equation model was conducted on a sample of 1079 young Italian cheese consumers. The results allowed us to confirm the hypothesized impact of CP on PPS through the mediation of PT and, particularly, SP. SP has a crucial communicative role in the model, demonstrating the ability to enhance the perception of the safety of TFPs. This research adds to the knowledge in the field of TFPs, focusing on communication and sustainable packaging as crucial factors conveying healthiness, nutritiousness, and perceived safety, consequently leading to a greater diffusion of the products themselves in the market.