You definitely DO NOT want to go shorter on the shock, unless you compensate with the dogbones (go shorter, IIRC, to raise the tail of the bike).
But it can be more complicated than that. What is the stroke length of the Gixxer shock? If it is significantly shorter than the OEM piece you could run into problems with it bottoming out.
I'd also be a tad apprehensive about going softer than stock with the spring. One of the reasons the 1st gens have a reputation for a rough ride is that the stock spring is too soft. Couple this with a rising-rate linkage and the static sag puts the spring into the range where it has way too little leverage- it acts like it's a lot stiffer than it actually is. So you end up with a rear end that's essentially underdamped and oversprung.
This is why all the suspension gurus advocate for a stiffer than stock spring, generally in the 600-650 pounds/inch range, compared to approximately 500 pounds/inch for the stock piece.
Not saying it can't or shouldn't be done, just that it may not be as simple as a parts swap-out.