Well according to most historical evidence a rapier while mainly a piercing weapon due to its strength in thrusting did have a bladed edge. Many rapier masters were known for using it as a slashing weapon in this regard. This occured when they had them sharpened for this.
A standard 3.X Rapier does not include it having an edge to be used in this regard. So you could in regard to opening it as both piercing and slashing charge the price of making it Masterworked (300gp) which would open the idea that it was made in that regard. To even out this price for such a gain take away the standard +1 Bonus to Hit due to being Masterworked.
This should keep the price well within the ideal of what you are looking for. And for an added 50gp you could add a basket hilt allowed the character to use it for blungeoning doing damage as if it were a Gauntlet.