Can a paladin use the two-weapon fighting style?

According to the online basic rules, the fighting styles for Paladins are: Defense (AC bonus with armour), Dueling (damage bonus with a single one-handed weapon), Great Weapon Fighting (damage reroll for two-handed/versatile weapons) & Protection (use your shield to protect others).

Is this an exhaustive list for Paladins? Am I allowed to take a fighting style offered to Fighters or Rangers?

My Paladin wields two shortswords, but none of the styles reward duel-wielding; I’m forced to take Defense. It’s certainly not bad, but I’d rather have the Two-Weapon Fighting style so that both weapons have a STR modifier damage bonus.

Alternatively, could I say I’m normally wielding one sword and so use Dueling, and then draw & attack with the second for my bonus action? This would only give +2 total extra rather than +STR total extra, but it’s better than nothing…