How can a patient deal with wudu’ (ablution) while being treated for a skin disease that requires medication to remain on the face and head for 24 hours over several months?

If water affects the medication, worsens the illness, or delays healing, then wipe over the medication if possible. If wiping over it spoils it, then place a splint over it and wipe over the splint. If wiping is not possible, then wash the healthy parts, then perform tayammum (definition) for the remaining parts after ablution, in accordance with the Almighty’s saying: (So fear Allah as much as you are able). An exposed wound should be washed; if that is not possible, then wipe over it; if that is not possible, then perform tayammum. A covered wound should be wiped over; if wiping harms it, then perform tayammum.