Normally Skin diseases are spread by scratching the affected areas. You are actually transferring the germs to other parts of your body that come in contact with your hand. So you need to be very careful. Try to keep the affected area clean. Also do not scratch it. Even if you do make sure you don't touch any other part of your body. Wash it thoroughly before you do anything else. Since this wouldnot be possible try avoiding scractching the affected area.
Skin cancers are not usually spread by scratching, germs may be, but skin cancer is not a germ. Ask your oncologist to re examine the areas. Radiation can cause drying of the skin and lead to itching.Your Radiologist should be able to prescribe something for the itching