Cross-chain blockchain protocols are essential for enabling interoperability and scalability by facilitating atomic asset transfers and secure data exchange across heterogeneous chains. Hash Time-Locked Contracts (HTLCs) provide the cryptographic foundation for trustless atomic swaps, but conventional HTLC schemes face significant privacy limitations. Issues such as linkable addresses, identity traceability, and transaction observability expose users to deanonymization and adversarial analysis in untrusted environments. To address these challenges, we propose ES-HTLC, a Hash Time-Locked Contract scheme based on enclave agents and stealth addresses, which integrates Trusted Execution Environments (TEEs) with stealth address techniques. ES-HTLC employs enclave-based proxy computation to conceal sender identities and utilizes stealth addresses to protect receiver anonymity, forming a decentralized dual-privacy model. Critical cryptographic operations, including randomness generation, ephemeral key handling, and hash value computation, are securely performed within hardware-isolated enclaves. This design enhances privacy, strengthens data confidentiality, and improves the security guarantees of cross-chain atomic transactions in decentralized blockchain ecosystems.