Eborcim,
I cleaned a few of my old Craftsman and Excelite screwdriver handles, and put them all in a tool box drawer together a few months back. That was a bad idea...as it seemed to accelerate
(or at least concentrate) the "stink."
Whew! 
So now I have them stored in a cardboard box out in the open air.
In my experience the white scum comes back over several months. But as the plastic gets older, it seems to occur sooner.
Right now my plan is to eventually sell all my Craftsman and Xcelite screwdrivers, and replace them one at a time whenever I find superior screwdrivers at yard sales, etc.
(I happen to really like older MAC screwdrivers with wood handles, though I concede that they aren't as durable. But I have found a few Matco drivers, and I really like them.)
I find that the general public holds a very high opinion of Craftsman tools, and is often unaware of Matco, Cornwell, and
(to a lesser degree) Snap On and Mac. So eventually these brands will probably fill the screwdriver drawer in my tool chest, instead of stinky Cman units.