I went so far as using a separate mixer to bring effects in (reverb, echos, etc). I don't "bypass" these effects, I just shut them off. The dry sound comes into the mixer in its own channel, so there's nothing to color it.
You can only do this with additive effects, though--the digital whammy is a pitch shifter, so there IS no dry tone. Pitch shifters tend to make the bottom end go away if they aren't real good--that's why it sounds more trebly. No bass.
I'd skip the effect entirely--how often will you use it? Why screw up your tone 98% of the time for an effect you'll only use 2% of the time?