As an efficient neural network model for graph data, graph neural networks (GNNs) recently find successful applications for various wireless optimization problems. Given that the inference stage of GNNs can be naturally implemented in a decentralized manner, GNN is a potential enabler for decentralized control/management in the next-generation wireless communications. Privacy leakage, however, may occur due to the information exchanges among neighbors during decentralized inference with GNNs. To deal with this issue, in this paper, we analyze and enhance the privacy of decentralized inference with GNNs in wireless networks. Specifically, we adopt local differential privacy as the metric, and design novel privacy-preserving signals as well as privacy-guaranteed training algorithms to achieve privacy-preserving inference. We also define the SNR-privacy trade-off function to analyze the performance upper bound of decentralized inference with GNNs in wireless networks. To further enhance the communication and computation efficiency, we adopt the over-the-air computation technique and theoretically demonstrate its advantage in privacy preservation. Through extensive simulations on the synthetic graph data, we validate our theoretical analysis, verify the effectiveness of proposed privacy-preserving wireless signaling and privacy-guaranteed training algorithm, and offer some guidance on practical implementation.