You should remove the mute too (or it'll be flopping 'round loose inside), which means taking off the tailpiece, which means de-stringing (well, de-tuning and taking them off the tuner posts, you don't have to pull them out of the tailpiece).
Also, the earth wire is soldered to the base of the mute assembly, so you have to shift it.
When putting the tailpiece back on, tighten the tailwards 2 screws first and don't over-tighten the 3 screws in the bridge well, or you can cause tail-lift.