Difficult to believe, as a rapier is VERY flexible, and its ability to flex and bend while in use is what determines the ways it is used, and what makes it different from more rigid sword designs.
What makes it different is the fact that it's a very long sword used primarily for thrusting. And it couldn't be "VERY" flexible because it had to be strong enough to give a solid thrust and parry in turn. Your description makes me think of a http://en.wikipedia.org/wiki/Sabre_%28fencing%29#The_weapon of some kind, as most professional fencing weapons tend to be flexy. (See the passage about strength http://www.thearma.org/Youth/rapieroutline.htm for more information. Also see opening description of a rapier as "rigid".)
Cyrus uses a sabre and both thrusts and swings like a bastard (depending how you play him). I'm not completely sure about sabres, but the term itself seems quite nebulous, and it could refer both to a straight thrusting sword, as indicated by modern fencing sabres, or slashing sword, as befits their historical use by cavalry. And in fencing, a sabre can be used to score with its edge, as opposed to the foil or epee. Ergo, Cyrus uses a sabre like a sabre.
But if you want a really bendy sword, I'd love for the Indian http://en.wikipedia.org/wiki/Urumi, a sword flexible enough to to be used as a belt, to be http://www.youtube.com/watch?v=gzxtpg9HKbU by the Redguards, since it's both cool and relatively unknown to the west.