Perspective, perspective, perspective.
One man’s gentleman is another man’s snoot, their superior, their elitist upperclassman more concerned with maintaining their reputation and snobbish mannerism than involving themselves with the dirty people they consider to be utterly inferior.
The chivalrous top-of-the-hierarchy nobles could care less about what the peasants think and more about matters concerning themselves or those above them, preserving a long, unjust tradition of corruption benefitting those in power by taking from those below them as darkness takes from light around it. Corruption has always been shown as a dark, shadowy energy. Tradition is always the shadow that follows behind us as we move forwards. Selfishness reflects the solitary aspect of Shadow.
What element is more greatly reminiscent of the classic tyrannical villain who never wish to dirty their hands with anyone they deem unworthy of their personal, superior involvement than Shadow? Shadow is not something like Metal where it’s all about roughhousing and destruction or like Plasma where it’s about energetic hype. It can be much more reserved, or much more devious depending on how one sees it.
How many other weapons reflect this same high-class “oh-so-pure” impression these villains may give off better than a rapier? A rapier is a symbol of status more than anything else.
Even the way a Rapier is used fits perfectly. Rather than heavy, aggressive wide sweeps, graceful impaling thrusts or swift slashes with much finesse, that suggest killing with ease especially considering how in some media rapier users will literally just put one hand behind their back. Impaling opponents is also much more intimidating, scary, and cold-hearted than slashing them, so even despite this mostly emphasizing Shadow’s more reserved, elitist, and corrupt aspects, the sheer aspect of cold-bloodedness isn’t lost through the Rapier as the impaling motions still promote such a feeling (see Palpatine’s fighting style, the jabs are very perfect for a sith-lord).
Also look at how Shadows often manifest themselves in games. Sharp tendrils or wispy strands.
The rapier handle if very fitting for this with its thin metal designs from the hilt. I can easily imagine the design constantly writhing as the user prepares to strike.