"But I am left handed..."

For the left-handed kenjutsuka: The way that the sword is worn does not change, nor the way the sword is drawn or held. Kihon do not change, nor do waza. The sword was worn on the left and drawn to the right because of a social more, and all schools of kenjutsu are built around that ingrained social requirement.

This is extant in our own society now; left-handed drivers do not get to drive on the left hand side of the road (unless you are in Britain). Auto dealerships are prohibited from selling right-hand drive vehicles in the United States.

There are many techniques in many ryuha (especially koryu) designed for left-hand forward, and all of the techniques can be mirrored right to left. Nukitsuke can even be performed left-hand forward by simply grasping the tsuka near kashira when beginning.

But when you think about it, kenjutsu (and any style of two-handed sword work) is really bilateral by its very nature. No real need to differentiate.

What does change is the way the waza are performed and the emphasis placed within them by the kenjutsuka. Right-handed swordsmen have a natural bias toward counter-clockwise movement while left-handed swordsmen move clockwise. Because of the dominance of the left hand control of the blade is shifted more toward the kashira, and left-handed swordsmen tend toward a more circular sword movement during kumitachi.