All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The formula that you mentioned in supplicating for a sneezer, which is (bless you), meaning ‘may Allah bless you’, there is nothing wrong with it.
The supplication for a disbeliever with blessings is permissible.
Ash-Shabramelsi said in a footnote on Nihayat al-Muhtaj: There is disagreement about the desirability of the supplication for the disbelievers, and ar-Ramli sanctioned that it is permissible. I think that he said: ‘It is not forbidden to supplicate for a disbeliever for forgiveness, unless someone wanted forgiveness for him [disbeliever] after his death as a disbeliever.
What is reported in the Sunnah is to say to a disbeliever sneezer the phrase: “May Allah guide you and render sound your state of affairs.” The evidence for this is what al-Bukhari narrated from Abu Moosa who said: “Jews used to sneeze in front of the Prophet expecting him to tell them: “May Allah have mercy upon you”, but the Prophet used to tell them: “May Allah guide you and rectify your affairs.”
An-Nawawi said in his Fatwa: “As for supplicating for a sneezer [i.e., for a non-Muslim who sneezes], it is desirable to supplicate by saying to him: “May Allah guide you”, as mentioned in the Hadith.
However, as long as this phrase [i.e., ‘bless you’ – the expression that you mentioned in the question] is used in supplicating for a sneezer and there are no prohibitions in it, then there is no objection to using it.
Allah knows best.