If you can play this study beautifully, using your own fingering, any fingering, that should be good enough. But where it fits the hand, why not use 4? I'm looking at the Cortot edition (highly recommended; his fingering in particular is generally very very good), and in the very first bar the first pair of octaves is marked 5-5, the second 5-4. All of these are staccato, so there should be no problem hopping up from Cb to Cnat with 5-5, but coming down Eb-Db, then 5-4 seems more natural (to me). But this all depends on your hands.
FWIW, Cortot's introduction to this study says: "...demands a refined, humorous, somewhat carefree performance... (tone quality) precise and light". That's what you have to aim for. I really can't see that whether pedal is marked or not should affect the fingering.
Which edition are you using, by the way?