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In this paper, we consider an edge cache-assisted millimeter wave cloud radio access network (C-RAN). Each remote radio head (RRH) in the C-RAN has a local cache, which can pre-fetch and store the files requested by the actuators. Multiple RRHs form a cluster to cooperatively serve the actuators, which acquire their required files either from the local caches or from the central processor via multicast fronthaul links. For such a scenario, we formulate a beamforming design problem to minimize the secure transmission delay under transmit power constraint of each RRH. Due to the difficulty of directly solving the formulated problem, we divide it into two independent ones: {\textit{i)}} minimizing the fronthaul transmission delay by jointly optimizing the transmit and receive beamforming; {\textit{ii)}} minimizing the maximum access transmission delay by jointly designing cooperative beamforming among RRHs. An alternatively iterative algorithm is proposed to solve the first optimization problem. For the latter, we first design the analog beamforming based on the channel state information of the actuators. Then, with the aid of successive convex approximation and $S$-procedure techniques, a semidefinite program (SDP) is formulated, and an iterative algorithm is proposed through SDP relaxation. Finally, simulation results are provided to verify the performance of the proposed schemes.