Is it permissible to give zakat to the needy wife of a paternal cousin, who openly refuses to accept zakat, by giving her money as a loan and then forgiving part of it with the intention of zakat?

If a person usually does not accept zakat, then it is not permissible to give it to him without informing him that it is zakat, lest something he dislikes enters his possession. If the woman explicitly states that she does not accept zakat, then either you try to persuade her to accept it, or you give her what she needs as a form of charity (sadaqah) or a gift (hiba). Informing the poor person that the money is zakat is not obligatory except in this specific case mentioned.