It almost looks like a pretty ordinary saber to me. Except that the entire cutting edge has been removed, leaving only a very small piercing tip at the end. Piercing blades do exist, but they still have edges to help them cut deeper. With a thrusting sword, depth of the thrust is what determines the damage.
The curve of this sword is very slight, but if you have a pure thrusting sword any curve is pointless and a straight blade would always be better. Also, the tip only has an edge on one side, while the other side is not sharpened. That's the case with katanas where thrusting is very much secondary. But on a pure thrusting sword with little weight, you really want both sides sharp.
Unless this started as a katana that had half its blade sawed away, a blade like this wouldn't actually curve at all during the forging process.
She really should have just gone with a regular rapier. This blade shape serves no purpose.
With no other information, also a rapier. If the hero has one its probably the standard sword style for the setting, and so most people would use them.
The sword was originally a katana that she modified and due to Japan's social bubble, I'm not sure they could have rapiers (this takes place before the 20th century)