Park microgrids, valued for their efficiency and flexibility, require privacy-conscious energy management to ensure a trusted scheduling and trading environment. This paper, focusing on park microgrids with shared energy storage, designs an energy management strategy that comprehensively considers shared energy storage, scheduling transparency, and privacy security. First, a blockchain-based energy management platform is established, forming an energy dispatch consensus committee to execute decentralized scheduling management and decision-making. Next, an optimized energy scheduling smart contract for park microgrids is designed, considering Time-of-Use (ToU) pricing and storage arbitrage to formulate the day-ahead electricity purchase and sales plans as well as the shared energy storage operation plans. Then, a privacy protection strategy based on the Shamir secret sharing scheme is proposed, effectively preventing data leakage during blockchain interactions. Finally, through case analysis, the superiority of the proposed method in microgrid optimized scheduling, data tamper-resistance, and privacy protection is demonstrated.