It's possible, but not ideal. You'll lose out on one of your biggest damage boosters, and take a pretty decent penalty to attack rolls.
A human swashbuckler (Inspired Blade) gets both weapon focus and weapon finesse for free, and can than take Fencing Grace and Two-Weapon Fighting, and at 3rd level take Two-Weapon Grace. Build from there as normal for a two weapon fighter, and rock dual Rapiers.
At 5th level, your build would probably look like this.
1st - Weapon Finesse, Weapon Focus (Rapier), Fencing Grace, Two-Weapon Fighting
3rd - Two-Weapon Grace
4th - Weapon Specialization (Rapier)
5th - Martial Focus (Light Blades) or Combat Reflexes
You'll want to invest in an Effortless Lace, and other normal Dex-Boosting items and such as normal.
You'll have 4+dex to damage, and a net -2 to attack rolls.
LG Human Swashbuckler 1/Oathfbound Paladin: Vengeance 11
On a 20 point buy, that's about Str15+2(h), Dex 12, Con 14, Int 8, Wis 8, Cha 16.
1:Artful Dodge (int is dex for prereqs)
S:Weapon Finesse (also cha is int(is dex) for prereqs)
9:Improved Critical: Shortsword
Unfortunately, Precis Throw only allows you to use Precise Strike at range but doesn't remove the only attacking with one hand restriction.
If you're okay with building around hitting multiple opponents, you could use Startoss Style and it's chain and get Precise Throw and be able to use Shot on the Run.
A basic build would look like this.
1st- Weapon Finesse (bonus), Weapon Focus (starknife), Starry Grace
3rd- Point-Blank Shot
4th- Precise Shot (bonus)
5th- Startoss Style
7th- Startoss Comet
8th- Startoss Shower
This build would come online a lot faster with a few levels of fighter, but that's up to you. If you do go the fighter dip route, you could take Dodge, Mobility and Shot on the Run and take advantage of maneuverability.