I say, with Allah's guidance: It is permissible if the illness is caused by using water, as informed by a trustworthy Muslim doctor. It is not required to fear death because dry ablution is allowed if water is sold at an exorbitant price, and the harm of worsening the illness is greater than the harm of increased cost. Therefore, dry ablution is permitted for this reason, as Allah says: {And if you are ill, or on a journey, or one of you comes from the place of relieving himself, or you have contacted women and do not find water, then seek clean earth and wipe over your faces and hands with it.} [An-Nisa: 43]. See: Sharh Al-Wiqayah p.105, Fath Bab Al-Inayah 1: 110, and Al-Tabyin 1: 235. And Allah knows best.