Will a 6ah battery work on my Kawasaki?

I'm trying to cut size and weight for my kawasaki kz400 cafe racer. I believe the manual calls for a 12v 12ah battery. I can't find one with 12ah thats small enough. I found a 13v 6ah anti gravity lithium battery that is the perfect size. Someone told me they used this battery on their honda cb350 but i think they switched to kick-only. If I were to switch to kick-only, would this battery work? Here is the link: http://www.amazon.com/...008LXULV6/

Kick-only hardly needs a battery at all.