This paper derives the capacity region of the 2- user symmetric linear deterministic Z-interference channel (Z-IC) with limited-rate unidirectional cooperation between the transmitters and secrecy constraints at the receivers. The proposed achievable scheme uses a combination of transmission of random bits and interference cancelation. A novel outer bound is derived, based on carefully selecting the side information, and partitioning the encoded message/output depending on the relative strength of the signal and the interference. The derived bounds match, thereby characterizing the secrecy capacity region of the symmetric Z-IC with unidirectional transmitter cooperation. Interestingly, it is found that, in the weak/moderate interference regime, the capacity region does not decrease due to the secrecy constraint at the receiver. Hence, the proposed scheme achieves the capacity of the Z-IC for the weak/moderate interference regime with and without secrecy constraints at the receivers. The results highlight the role of the unidirectional transmitter cooperation in facilitating secure communication over a 2-user ZIC in the high interference regime.