This paper explores the physical-layer security in a small cell network (SCN) with cooperative cache-enabled small base stations (SBSs) in the presence of randomly distributed eavesdroppers. We propose a joint design on the caching placement and the physical-layer transmission to improve the secure content delivery probability (SCDP). We first put forward a hybrid caching placement strategy in which a proportion of the cache unit in each SBS is assigned to store the most popular files (MPFs), while the remaining is used to cache the disjoint subfiles (DSFs) of the less popular files in different SBSs as a means to enhance transmission secrecy and content diversity. We then introduce two coordinated multi-point (CoMP) techniques, namely, joint transmission (JT) and orthogonal transmission (OT), to deliver the MPFs and DSFs, respectively. We derive analytical expressions for the SCDP in each transmission scheme, considering both non-colluding and colluding eavesdropping scenarios. Based on the obtained analytical results, we jointly design the optimal transmission rates and the optimal caching assignment for maximizing the overall SCDP. Various insights into the optimal transmission and caching designs are further provided. Numerical results are also presented to verify our theoretical findings and to demonstrate the superiority of the proposed caching and transmission strategies.