Wedge it

This Tremolok contraption is what I use every time I re-string my Floyd-equipped (or its derivatives) guitars. Everywhere else, players were warned not to remove all strings simultaneously for various apprehensions which I do not wish to invoke. I make it a point to remove all strings so I have access to the fretboard- I need to clean it. 

On other days, any pencil would be a good substitute :-D

Pencil stopper

The prevailing reason- for us guitar owners dealing with a dual-action, locking whammy bridge- for not removing all strings from the bridge during a re-string exercise, is the bothersome collapse of the bridge into its cavity.When this happens, we cannot access the locking end of the bridge to free the strings from the clamps.

You can use a pencil or any other firm contraption to wedge it between the bridge & the cavity. Do lay a piece of cloth under the pencil to prevent it from denting the body surface.