In decentralized finance (DeFi), conditional payments are crucial for applications such as insurance and phased project payments, where funds are transferred based on specific event outcomes. However, such systems face two major challenges: (1) ensuring fair exchange between mutually untrusted parties and (2) eliminating the single point of failure in both payment authorization and event outcome verification. To address these issues, we propose a new cryptographic primitive called Dual-Threshold Verifiable Witness Encryption for Signature (DTVweS), which applies threshold cryptography to both signers and adjudicators. This scheme allows signers to encrypt their signature shares and the full signature is only released when a threshold number of adjudicators have attested the outcome of the event. Additionally, we present two efficient constructions of DTVweS for Schnorr and BLS threshold signatures. By utilizing non-interactive zero-knowledge proofs, our scheme eliminates the need for expensive cut-and-choose techniques, thereby reducing the communication overhead and enhancing both security and efficiency.