Look, with the only guidance "is this the OPTIMAL build" but without telling us what you are trying to optimize, we can just guess at your goals.
If you're looking for THE Min/Max undead army, you're not doing anything special besides maxing Chr. It's nice, but nothing special over other oathbreakers.
If you're looking for the THE Min/Max damage, it's not close. Oathbreaker misses many of the advantages of other paladin oaths that race for Great Weapon Mastery (advantage of bonus to attack), but that doesn't mean that even within Oathbreaker you can't do better. Dex and TWF without multiclassing to get the Two-Weapon Fighting style (not offered to paladins) and without the Dual Wielder feat doesn't do a lot of damage. Now, three attacks is nice for nova damage, but having played a paladin you will run out of spell slots for Smites well before you run out of attacks for the day. If you do want to spend the feat, spending the same feat on Polearm Mastery and going STR instead would still be a big jump over TWF without the fighting style, plus give you more reaction attacks, more damage on an opportunity attack, reach, and only needing one magic weapon.
You are doing well on defenses. Not THE Min/Max, simple plate gives AC 18 vs. Studded Leather + 20 DEX of AC 17. Dual Wielder feat would allow you to pull even. All paladins do well on saves thanks to their auras, you do significantly better than most on Dex (damage) saves, are proficient with CON saves, and your only weakness among the big three saves is Wis (control) without proficiency or bonus. But with your paladin aura you're still doing fine.
Fallen Aasimar, as you mentioned, give +1 STR which doesn't help your dex build. Because of the nature of point-buy, putting that to your lowest vs. one of the highest will make a big difference in the value of your ability scores. Darkvision is nice. Healing Hands rather overlaps your lay-on-hands. Necrotic Shroud is a nice once per day power, though you need to be careful not accidentally scare your allies. Also it takes an action to trigger so it is likely that you won't make up that action's lost damage potential with the bonus damage.
Now, all of that - forget it. It's a cool build and I'd have fun playing it. It may not be "the OPTIMIZE build" but it hangs together mechanically and I like your whole piracy angle. Enjoy your concept.