Sex conversion in speech involves privacy risks from data collection and often leaves residual sex-specific cues in outputs, even when target speaker references are unavailable. We introduce RASO for Reference-free Adversarial Sex Obfuscation. Innovations include a sex-conditional adversarial learning framework to disentangle linguistic content from sex-related acoustic markers and explicit regularisation to align fundamental frequency distributions and formant trajectories with sex-neutral characteristics learned from sex-balanced training data. RASO preserves linguistic content and, even when assessed under a semi-informed attack model, it significantly outperforms a competing approach to sex obfuscation.