You COULD use a hard-wired bypass . . . you'd need an a/b box. Take your signal from the guitar (or whatever pedal is just ahead of the whammy), split with one output going into the whammy input, the other into "in A" in the a/b box. The output from the whammy goes into the "in B" in the a/b box. The "out" from the a/b box continues into the signal path. Clicking the a/b box takes, then, either the dry guitar signal, OR the whammy output, without using the whammy's bypass.

Only problem is that you'll have a "click" in your sound whenever you switch, but you probably won't be able to hear this over the band, in a live situation. Kinda klunky, but it'll preserve your dry tone.