There is a person who suffers from a skin allergy triggered by any cold. When any of his limbs—such as the…

There is a person who suffers from a skin allergy triggered by any cold. When any of his limbs—such as the forearm or the leg from the knee to the foot—are exposed, he experiences such a reaction that it can even lead to choking. As a result, performing ablution (wudu) or full ritual washing (ghusl) with water is impossible for him, and if he tries to perform tayammum (dry ablution), he also experiences a reaction and suffers. Therefore, he is unable to perform wudu and is affected by tayammum every time he prays or daily. What is the ruling here regarding prayer and purification?