Is it permissible to swear a false oath to avoid the execution of the Sharia-prescribed punishment, knowing that the fornicator has repented and the woman is threatening him by claiming that he raped her?

If a man did not force a woman into zina (unlawful sexual intercourse), and she falsely claims that he did, he is permitted to swear an oath that he did not coerce her, and he would be truthful. If he is asked about engaging in zina willingly, he may use ta'rid (ambiguity) and tawriyah (double entendre). Indeed, he is allowed to lie to conceal himself, such as denying the sin to conceal himself or others, unless the other person has openly committed it.