You're required to stick to books you own in PFS anyway. The classic Dex halfling is a rogue with weapon finesse who uses daggers and relies on sneak attack to add damage. Not the most optimal damage-dealer, to be frank. The only dex-to-damage feat in the main RPG line is in the Advanced Class Guide; the rest are all in campaign setting books.
Ways to add damage without that using the books you have:
River Rat trait (+1 damage to any attack with a dagger): Extremely useful for builds like this.
Weapon master fighter: take at least three levels of this, and it will get you two useful feats, and weapon training, which you can boost with Gloves of Dueling.
Magus can be built to be dex-based, and rely primarily on spells to do damage. With a rapier, this can be fairly effective, but you'll be a nova build -- when you run out of spells, you're poking the baddies for 1d4 damage per hit.
Ranger can make it possible for you to get power attack without having to have a 15 strength before racial adjustments, and adds static bonuses to attacks against certain enemies, and eventually lets you use the spell Instant Enemy to apply these against any foe.
Options that require buying additional books from the main RPG line (keep in mind you can buy any of the hardbacks from the RPG line for $9.99 in PDF form):
Whetstone: You can sharpen any non-magical blade with a whetstone for 15 minutes and get a +1 to damage on the first successful attack. (Ultimate Equipment)
Knife master Rogue: gives 1d8 sneak attacks instead of 1d6 when using daggers or similar weapons. Makes a nice combo with weapon master fighter. (ultimate combat)
There's a rather unique build that combines the Terrain mastery rogue talent from Ultimate combat with the Horizon walker prestige class from the APG. Too complicated to explain here, but you can use the search function of the forums to look for it.
ACG offers the best option for dex-to-damage without having to buy lots of books. Swashbuckler + slashing grace lets you use a one-handed slashing weapon with dex to attack and damage; however, you can't get those until level 3, or level 2 if you dip fighter or some other class that gives you extra feats.
A slayer or ranger might be best, mostly because they can get TWF at level 2, and you can use your 1st level feat for finesse.
Slayer looks like it can get better consistent attack/damage, while ranger can get more extreme attack/damage against favored enemies (humans and evil outsiders are always a good bet).
A dawnflower dervish bard is suprisingly good too. They might give you dervish dance for free first level, but with double bonuses on inspire courage (which brings it up to rage levels), TWF or archery is a much more effective style (going scimitar early on until you get your feats together is a good idea though). I suppose archaeologist bards with fate's favored have similar advantages.
Halfling swashbuckler 1/ paladin X
Slashing grace at level 1 with kukris. Then at 3 is TWF.
Level 5 can be risky striker. Then finish out with improved TWF and Improved critical.Enjoy!!
Sorry, that doesn't work. On multiple levels.
Slashing grace only works on 1 handed weapons. That was likely a conscious design decision to make it difficult to get dex to damage with TWF.
Also, as far as I am aware, halflings cannot get slashing grace at level 1. You need 2 feats open to do that (weapon focus and slashing grace itself). They can do inspired blade and fencing grace, since that archetype give a free weapon focus.