The secrecy rate of Wyner wiretap channels is analyzed for general classes of sources, sensing schemes, and channel distributions. Using the replica method, heuristic closed form expressions are obtained for the asymptotic secrecy rate as a function of the statistics of the system model. This result is then applied in practically oriented scenarios, leading to expressions that expose the existing trade-offs between system parameters and security requirements, including the region in which perfect secrecy is feasible. As a particular example of the broad class of sources that are considered in the main contribution, source distributions giving rise to sparse signals are studied. In that setting, the secrecy rate linked to the disclosure of information about the support of the signals is investigated.