I have never owned a Floyd style git and I thought I read somewhere that it was a fallacy that you had to cut the ball off of a string?
Well, you could always thread the string the wrong way round so that the ball ends are at the headstock - that way you wouldn't
need to snip them off (though it would look untidy IMO)
As MMM states, some Ibanez models don't require the balls to be snipped, IIRC the early Yamaha Pacificas were bottom loaded too. There was also a superb floyd-style trem from Fernandes in the 80s where the strings were rear loaded (why, oh why did I sell that guitar?!? :()
However, the original Floyd, Schaller Floyd & most derivatives require a plain string end to be inserted into slots where they are clamped in place by an small block pushed by an allen screw.
Joe's Scheter doesn't seem to have a Floyd, but some sort of bottom loaded trem with fine tuners & a locking nut...