I posted a similar "no Komnenian Restoration" thread a few months ago, but, sadly, it got no traction
Anyway, i would expect whoever's the West's puppet Byzantine emperor to still order a crusade of sorts against the Turks. I would expect such alternate First Crusade to have less potential for success than OTL, due to the lack of Alexios' strengthening of Byzantine finances beforehand. Furthermore, if Malik Shah I's death is butterflied away, then the First Crusade is likely to fail already at Dorylaeum.
No Alexios Komnenos could also lead to Tzachas, a Turkic bey who commanded a large fleet at Smyrna, being more of a threat.