Is it permissible for me to marry my paternal cousin while I am her guardian, knowing that there is no one else who can take my place in her guardianship?

If the woman's guardian (wali) in marriage is her paternal cousin and he wishes to marry her, and she consents, there is no objection to that. He can personally conduct the marriage contract for himself and for her by saying: "I have married you," or "I have married myself to so-and-so (mentioning her name)," and he does not need to say "I accept." He can also appoint a man to marry her to him, in which case his representative would say: "I marry so-and-so (naming the woman) to you," and he (the groom) would say: "I accept." Witnessing the contract is obligatory in both cases.