Here's an alternative to the Floyd lock nut and string retainer. Graphtech sells a nonlocking replacement nut that is made to fit in the floyd lock nut mounting holes. You'll also need to change to locking tuners, I used Sperzel as they have staggered string thru holes which eliminated the need for the string retainer.
Although the Sperzels are heavier then the stock vintage style tuners the overall weight is about the same as the new nut is much lighter and the string retainer removed.
I believed this mod corrected a number of problems the guitar had and removed the need for the small hex wrench.
I was never a huge fan of the locking tuners but in this instance they are a great improvement. I'm sourcing parts for a new guitar with a floyd right now and I'm going to use a regular strat neck with Graphtech nut and Sperzels, that's how good it worked.