Peace be upon you. According to Grand Ayatollah Sistani (may Allah protect him), it is not necessary to remove dry skin and wash underneath it. However, if the skin is considered an external layer, it must be removed. According to Grand Ayatollah Khamenei (may Allah protect him), for skin conditions like warts, as long as the outer layer remains, it is sufficient to wash the surface, and there is no need to ensure water reaches underneath the skin. Even if part of the skin is cut and some remains, it is enough to wash the surface of the remaining part, and it is not required to remove it entirely. May you be successful in all good.