A rapier is always a flat bladed weapon. Pretty much like the side sword. And the last 9 inches of the blade is thin and razor sharp. Its designed to cut tendons at the joints of you opponent. No blunt damage on a rapier.
Meaning it has a slash. Give it everything except an overhead and I think this idea could turn out to be quite interesting.
Here's my take on the stats:
Cost: 11,000
weight .75
requirement 6
spd rtng 102
weapon length 110
swing damage 22, cut
thrust damage 34 pierce
Cannot be used with a shield
Tempered = 103spd 23cut 35pierce
Balanced = 104spd 24cut 36pierce
Masterwork = 106spd 25cut 37pierce
With the extreme light weight and use without a shield, you're going to get stunned constantly. This being the downside to a brutal thrust. I like the idea of there being a 1h that's meant to be used without a shield.