Go and perform the Hajj with your wife . By nature woman is weak and could become the cause of strife and sin. This is why the shariat has not given permission for woman to travel without Mahram, whether it be religious or worldly journey. Paternal cousins and maternal cousins cannot be Mahram because marriage can be consummated with them. Mahram is such a person with whom one may not experience feelings which are natural only to a married state.
Some women consider anyone as brother or son for the sake of making a journey.
This is not allowed by Shariat. In the performance of the holy rites of Hajj to break Shariat law and perform the Hajj is clearly a sin and considered as haram. This is because from beginning to the end it is a violation of the Shariat. Without a Mahram a journey of 48 miles is forbidden whether the journey is by air or by any other means. If a woman is eligible to perform Hajj with the necessary means to do so but cannot find a Mahram she is not allowed to perform it.