You are asking a business question, not an English question.
Is it the person whose name appears on the letter asking you to do it? What is to keep you from handwriting a "pp" even if it's not typed there? You can sign your own name with the word "for" handwritten before the person's name in the signature block.
If the signature block was "Peter Parker" and anyone other than Peter Parker told me to sign Peter's name, I would refuse as well. If Peter told me to do it, I'd ask if he wanted me to use the "pp" or sign my own name and use the "for." Even so, I wouldn't sign Peter's name with no indication that it wasn't Peter who had signed it.