This could be done, but it wouldn't be all that pleasant a solution. The most effective scripts to use would be k_def_damage01 and k_hen_damage01. Theoretically every character fires one or the other every time they take damage, which means the scripts can be edited to apply additional circumstantial damage. I've used this method before for something else, so I can certainly say it would work. Alternatively, editing k_ai_master would also work, because both damage scripts fire the on damage event in the AI. The problem with all these, though, is mod compatibility. Any edits to them are going to be fundamentally incompatible with any other edits.
But if one were to go with that option, the script could check if the target's last damager has the particular feat, and if so apply extra damage equal to their dexterity modifier minus their strength modifier. in other words, have the damage bonus equal to the dexterity modifier if higher than strength.
This sounds too convoluted to be worth it. You have to pick a feat and then make and use a specific upgrade when you could go for another build and have an extra upgrade. Additionally, decreasing strength in this way would have unintended negative consequences. Strength is used for some item proficiencies and checks in dialogue.
Also, either way, I would suggest using the existing finesse feats rather than making new ones. They are next to useless on their own as it is, so if you're going to have to spend a feat, better to spend it on one that does something.