The ability to cut is determined by the angle of the wedge that makes the edge and it's smallest point, the materials the blade is made out of, and the force applied to the blade.
Hypothetically a flat chunk of jello can cut anything if you apply enough force to it. The reason it doesn't work is the forces acting on the material make it break up before it can do it. The Smallest point is the biggest point that has to get between the points on the other object, and the wedge is just how smooth and thus how much force is needed to push more of the material between the other material.
So there is no "ultimate design shape". If you could you'd want to just make Free Quark edged sword with an infinite gradient bevel to human sizes made out of the densest material in the universe equipped with an anti-gravity field to counteract the weight.
But you want shape... so, basically you want a straight blade always, because curves weaken the blade and as such make it easier break and lower it's overall threshold for actual cutting ability. Curvature of the blade is for depth of cut, not cutting ability. The more curved (to a point) a blade is the longer the cut is, because more of the blade is in contact with and passing through the area as it is going through the same motion for the wielder.
a slightly curved blade, like the Katana, maybe helpful in drawing the blade and inductive to certain styles of fighting, but it's overall a weaker blade in many respects due to that slight curve and the disadvantages outweigh whatever slight advantage that curve brings.
The more curved the blade is the more unwieldy it is to sheath and use in various other respects than just straight cutting so even though a greater curve causes a longer cut, I'd consider it a worse overall sword in general because it loses all those other things and is harder to sheath than a normal sword.
So again, best cutting sword possible, probably a backsword (single edged generally straight blade). Katanas, Falchions, and "backswords" fall into this category of sword. I've taken to calling them all backswords, now, because it makes the most sense.
As far as length of the weapon, that depends on the wielder. It's not a "standard" thing. For example, I like the feel of a Wakazashi vs the feel of a Katana simply based on length, because the swords otherwise are the same so for me I'd use say the "ideal" is a short backsword. Others however might prefer a long backsword like the katana or the standard backsword. Still others might prefer a dagger or a much longer sword.
Also after re-reading what you said, if the source of the cutting isn't the sword shape then I'd actually go for a thrusting or chopping based weapon design since the it's already got cutting maxed out. Such as the Rapier or a double edge long sword. I'd go thrust because they look better imo, and they are considered more noble and gallant, but choppers are more menacing. A brute of a villain might use a chopper style.