Huh. I never noticed the ACP section of the weapon finesse feat.
Since "Shield, light" appears in the "Light Melee Weapons" section of the Martial Weapons table (while Shield, Heavy appears in the One Handed Melee Weapons section), the light shield *IS* a light weapon when used for bashing and therefore can be finessed.
HOWEVER, note that the Weapon Finesse feat itself tells us that simply carrying (let alone wielding) a shield causes you to take its ACP on your attack rolls.
The Shield, Throwing appears in the Gladiator Weapons table under Ranged Weapons. That said, making a light shield into a light throwing shield does not mean it is no longer a melee weapon. I wouldn't allow dex to damage if you throw an agile light throwing shield as when used that way, it is NOT a melee weapon, but if you melee bash with it, you would get dex to damage.
Also worth noting is the Shield-Trained trait from Inner Sea Gods. It lets you treat Heavy Shields as light weapons. Get one made of Darkwood for 257 (267 with spikes) and it has no armor check penalty.
If you're Human, you can take the Shield Bearer character trait, giving you a +1 Trait Bonus on damage rolls with the Shield, and an intriguing ability to use 1/day.
I'd honestly suggest a Quickdraw Light Throwing Shield made out of Mithril. It's a bit more expensive, but it does reduce the weight, and would allow you to count it as Silver for the purposes of DR.
Plus the best part is it can't be eaten by termites or burned away via fire.
@ OP: Agile property RAW says this:
This special ability can be placed only on melee weapons usable with Weapon Finesse.
Agile weapons are unusually well balanced and responsive. A wielder with the Weapon Finesse feat can choose to apply her Dexterity modifier to damage rolls with an agile weapon in place of her Strength modifier.
The restriction only applies to the type of item it can be put on: melee weapons usable with Weapon Finesse. Is a Quickdraw Light Throwing Shield a weapon? Yes. Is it a melee weapon? Yes. (And a Ranged Weapon too, which doesn't discount the fact it's a weapon commonly used in melee combat.) Is it usable with Weapon Finesse? Yes, as it's a Light weapon. You also need to have the Weapon Finesse feat to activate this ability.
Per RAW, I don't see it being a problem to apply Dexterity to damage rolls when throwing a Throwing Shield, as it makes no distinction of what kind of attack is required to benefit from it. All it says is you need to have the Weapon Finesse feat in order to activate the special ability.
Per RAI, I can definitely see it being limited to melee only, as the intent behind this feature is to make Weapon Finesse a more attractive option to take (though it's actually just a trap), and not just let you turn your Ranged options into ridiculous overpowered monstrosities.
I'd make sure you ask the GM as to how he would rule it, but from a Rules as Worded standpoint, there's nothing wrong with applying your Dexterity to damage when using it as a Thrown weapon.
I'll also point out that if you want to use a Throwing Shield effectively, you do need to acquire proficiency, as making your shield a Throwing Shield makes it an Exotic Weapon, so you either need to spend a feat to get proficiency, or find some other way to get proficiency.
Halfling is a good race, but I'd suggest you pick the Sacred Shield Paladin archetype if you're going to pick Halfling, to make use of that Charisma.
**EDIT** Hobgoblin is even better, with a +2 to Dexterity and Constitution for free, without issues whatsoever. Even the Strix is damn amazing, since it gives you essentially free Flying.
While Agile can only be placed on melee weapons, it still works if you throw that melee weapon. So an Agile dagger can use dex to damage when thrown.
Huh. I think that is the first method I've seen for adding Dex to damage to a ranged attack. Combine it with the Sharding special ability and you could make ranged attacks with any finesseable weapon even if it can't normally be thrown. Estocs, Elven Curve Blades, and Elven Branch Spears come to mind. Using Legacy Weapon to add Sharding, an Occultist could pull this off at a fairly low level. Throwing copies of an Elven Branch Spear and getting Dex to damage sounds like fun.