All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If a non-Muslim sneezes, it is permissible for a Muslim to tell him: "May Allaah guide you and rectify your affairs." The evidence about this is that Imaam At-Tirmithi reported that the Jews used to sneeze in front of the Prophet expecting him to tell them: "May Allaah have mercy upon you", but the Prophet used to tell them: "May Allaah guide you and rectify your affairs."
However, if you are the one who sneezes and says 'Al-Hamdu Lillaah' and then a non-Muslim tells you: "May Allaah have mercy upon you", then we do not see any harm to respond to him saying: "May Allaah guide you and rectify your affairs." In reality, you are supplicating to Allaah to guide him, and it is permissible to supplicate to Allaah to guide non-Muslims.
It is confirmed that the Prophet supplicated for the tribe of Daws saying: "O Allaah! Guide the tribe of Daws." He also supplicated for the tribe of Thaqeef as he said: "O Allaah! Guide the tribe of Thaqeef." [Al-Bukhari and Muslim], and these two tribes were not Muslims at that time.
Allaah Knows best.