Question:
If one's skin around his nose is very dry to the extent that cleaning it with a tissue would likely cause dry skin to become dislodged in the process, what should one do if he wants to clean it on shabbos?
Answer:
Unless it will surely take of skin, it is not a psik reisha, and permitted. To try and prevent such an issue you can try applying Vaseline or some other cream to you nose before shabbos to soften and heal the skin around your nose.
Best wishes