Edge uses an Eventide harmonizer now for his shimmer. Prior to that, I believe he used an AMS delay/pitch shifter unit.
Although I don't think that the Digitech Whammy can handle the shimmer effect by itself, it can also be achieved using several Digitech products. The IPS33, IPS33b, and DHP55 (the one I have) all manage a good shimmer.
Unless you've just got lots of money to throw at a relatively specialized effect, the Digitech processors are a better bet than the AMS or Eventide, both of which are quite costly. Contrasted with the DHP55 (which I picked up used for $150), I think most Eventides go for around $900+, and the AMS was even more pricey, the last time I checked.
EDIT:
I just did a quick search on Ebay for various Digitech pitch shifter/harmonizers, and there are several on there, with the most expensive listed at $175. If you're after one, I'd definitely check over there.