Don't use water or glass cleaner.
Don't even think about wiping or cleaning the contats in the CPU socket. Those pins are very fragial and easy to bend.
Use rubbing alcohol to wipe the processor contacts.
Let dry and proceed with your assembly.
Static electricity is the main reason they say to not touch the contacts, but oils and acids in the skin don't do them any good.
In 28 years of working in this field, I have had 2 cases of ESD (static) damage caused by miss handling components and neigther were processors.
A light wipe with rubbing alcohol and you are back in bussness.