What is the ruling on performing righteous deeds and dedicating their reward to someone whose dignity and honor I have wronged, without confronting them about it, in order to avoid a greater harm? And do these deeds absolve me on the Day of Judgment?

It is sufficient, according to many scholars, to seek forgiveness for and supplicate for the person you spoke ill of, and to mention him in good terms where you mentioned him in bad terms. There is no need to seek his forgiveness directly to avoid potential mischief. The donation of the reward for acts of worship benefits the deceased by consensus. As for the living benefiting from it, there is a difference of opinion, but the relied-upon position of the Hanbali school is that they do benefit from it. If you limit yourself to supplication, seeking forgiveness, and mentioning him in good terms, that is good and absolves you of responsibility.