There are several difficulties with this.
First, there's the beads Kmt mentioned. 5 millenia and these tiny little things didn't rust away to nothing. Given the same conditions, a bulkier item experiencing the same rate of corrosion should still leave some significant traces then even after another 5 millenia.
Second, there's the artifact from the shaft itself. If it does in fact date from the construction of the pyramid and if that date is as old as claimed, The fact that it exists at all would tend to argue against the complete destruction of all such artifacts from the period.
Third, there's kmt's point about traces of rust. Iron, once oxidized, cannot oxidize further, so traces of even complete disintegrated iron artifacts remain in the soil as anomalous patches of rust. It has been possible in many archeological deigs to virtually reconstruct artifacts entirely from the shape of the rust traces left behind. If nothing else, the very presence of the rust speaks to the former presence of an iron artifact, yet we find none. One would think at the very least such a valued material would make it's way into grave goods even if scarce and certainly if not, given the other sorts of commodities which did.
Fourth, This is getting away from the apparent evidence of bronze usage in relation to stone cutting. If they were using iron or full-blown steel, why are there traces of verdigris in the various borings, etc, but not the aforementioned rust?