assalamu alaykum,
The title and the question are misleading. Sneezing is not an innovation, it is a natural reflex in case of dust allergy or illness. Ibn Umar never said that it is an innovation to sneeze. What could be said is that saying a salutation to the Prophet S each time you sneeze is an innovation.
When someone sneezes we say Alhamdulillah, which means all praise is for Allah.
The reply is YarhamukAllah, which means “May Allah have mercy upon you.” …and he (i.e. the one who sneezed) should reply back to him: Yahdeekumullah yuslih wa balakum, “May Allah guide you and rectify your condition.”
Bukhari No# 6224; Abu Dawud No# 5033; At-Tirmidhi No# 2741; Ibn Majah No# 3715
There is no mention of sending salutation upon the Prophet Muhammad S when sneezing. Therefore, to do so would be an innovation. We should say the correct duas at the right time in accordance with the Quran and authentic sunnah.
Wasalam