Answer
I say, and with God's success: It is disliked to use the right hand for clearing the nose; for Aisha, may Allah be pleased with her, said: "The right hand of the Messenger of Allah (peace be upon him) was for purification and food, and his left hand was for his needs and anything that was impure," in Sunan Abu Dawood 1/55, and in Sha'b al-Iman 5/77, and in the Sunan al-Kubra by al-Bayhaqi 1/113. Then, clearing the nose is for removing impurities, so using the left hand is preferred in this case, because clearing the nose is the act of snorting, which is expelling what is in the nasal cavity by breath, from what has dried of mucus — and the nasal cavity is the resting place of the devil; as he (peace be upon him) said: "When one of you wakes up from his sleep, and performs ablution, let him snort three times, for the devil spends the night in his nasal cavity," in Sahih al-Bukhari 3/1199, and in Sahih Muslim 1/212. See: Tabyin al-Haqaiq 1: 7, and the Hadiyya al-Alaiyya p. 26, and Allah knows best.