Dua e Qunūt

If a Shāfiʿī muqtadi (follower) reads Fajr ṣalāh behind a Ḥanafī imam, what would be best for the Shāfiʿī to do with regards to Dua e Qunūt? Can he shorten the qunūt? If he does shorten the qunūt, does he make sujūd al-sahw (the prostration of forgetfulness)? If he reads the entire qunūt and joins the imam in sajdah, does he still make sajdah?