thanks for all the replies guys. I looked at every system that was recommended in this thread, and a few more besides, but im still stuck on Shadowrun. A lot of the suggestions here have been great and im working on writing up a history that explains some of the magical stuff in non magic ways. Will post here if this campaign actually gets off the ground.
So, just to clarify.
You want a Shadowrun world, with Shadowrun Mechanics, but no magic at all?
No Metahumans?
No HMVV Plague?
No Surge?
No Magicians, Physads, Spirits, Spells?
No Orichalcum or magical minerals?
No Dragons?
Query: Are you allowing Technomancers?
In which case, it's actually really simple.
A) Remove every archtype or critter with a Magic attribute. Done.
B) Remove all races except Humans. Done.
C) Remove Great Dragons from head of boards, and replace with seemingly uber Human corporate leaders (or personal armies, in the case of Ghostwalker)
D) Rewrite history to account for Great Ghost dance effects etc as just Catastrophic geological phenomena (multiple volcanic explosions, etc)
Then fast forward to the current 2072 timeline, where noone really cares about the history anyway

and move on with Magic having never happened.
Personally, I really don't understand why you're doing this. Magic is a very cool, and integral part of the standard Shadowrun setting.
However, different strokes for different folks, and mechanically what you're doing is actually quite simple.
Cheers and good luck.