Know Your Customer (KYC) is a core component of the Anti-Money Laundering (AML) framework, designed to prevent illicit activities within financial systems. However, enforcing KYC and AML on blockchains remains challenging due to difficulties in establishing accountability and preserving user privacy. This study proposes REGKYC, a privacy-preserving Attribute-Based Access Control (ABAC) framework that balances user privacy with externally mandated KYC and AML requirements. REGKYC leverages a structured ABAC model to support the flexible verification of KYC attributes and the enforcement of compliance policies, providing benefits to multiple stakeholders. First, it enables legitimate users to meet compliance requirements while preserving the privacy of their on-chain activities. Second, it empowers Crypto-asset Service Providers (CASPs) to tailor compliance policies to operational needs, ensuring adaptability to evolving regulations. Finally, it enhances regulatory accountability by enabling authorized deanonymization of malicious actors. We hope this work inspires future research to harmonize user privacy and regulatory compliance in blockchain systems.