Is this the sort of lowering kit you're looking at? No dog bones on the FZ6 (unlike say the FZS600), so shortening shock like this is your option.
I fitted one of these MFW kits on my wife's CBF500 a while ago. It appears this FZ6 kit is pretty much same deal and same setup. And just like agricola mentioned, everything on our CBF was seized up like a bitch. Though that CBF had been run year round as commuter hack for 10 years with no rear hugger... Tried everything, freeze spray, flame, impact drill / hammer, the lot. In end had to squeeze a hack saw blade into hinge to saw it off... As the FZ6 has a hugger as standard, I'm surprised it also got that bad...
Be careful on compressing the spring, if it pings out you'll have someones eye out! There are proper tools for this job, bit brave trusting cable ties... :-) I took our CBF shock to AllBikeEngineering (near Blackwall Tunnel), who serviced it, re-gassed it, put new piston rod in and swapped on the MFW end piece for me (about £200 ish if I recall). Then obviously refitted with all new bolts, bearing, bushes etc. If I recall some of the original bearing parts aren't reused with the MFW link though.
Either way, it's held up fine for several years hence, my short arse wife is happy. Note we did also have to push front forks through yoke to match drop on rear. Then found bike stood way too upright on side stand, so that needed to be chopped down a re-welded (£50 job by local garage).
Full write up on my blog if you fancy reading more.