Is there anything in the Hebrew that would make any of these translations more accurate than the others? Is gender specified in the Hebrew? If so, is it specified in both places as "he" and "him"? What would be the reason for eliminating "he" but leaving "him"?
I hope to answer your question without getting ensnared in identity politics.
The facts: translations are never one-to-one or word-for-word. In the case of Ps 41:1, there is no pronoun "he" used, but it is a participle (in English we would say it is a gerund). And it is in the masculine gender. So a literal "translation" would be "blessed is the understander of the poor," that is, someone who understands poor people, or takes them into consideration, or some such. In the second case, the pronoun is indeed masculine: "the Lord will deliver *him*."
Hebrew grammar distinguishes between the masculine and feminine genders. But grammatical gender is not the same as biological gender. There is overlap, yes, but from culture to culture, from one era to another, those ideas change. Take a modern example: in English we refer to ships and boats with the feminine pronoun "she." But Russian speakers use the masculine gender. And the Germans use the neuter gender for "girl" (das Mädchen), whose biological gender is definitely female! One final example: in the Old Testament, the word ruach
, meaning "wind, spirit" is grammatically feminine. But sometimes, when the word is used to refer to God, the masculine gender is used by pronouns referring to it. Because the ancients normally referred to God with the masculine gender, we see that the writer/speaker is not thinking of "correct" grammar at that point, but is thinking of the person to which ruach
In the case of Ps 41:1, the use of the pronoun or not makes no difference to what is being said. "Accuracy" is in the eye of the beholder. That is why I decided to learn Greek, Hebrew, Aramaic (and a number of other languages!) thirty years ago. So that I would not be dependent upon any translation or commentator for a clear understanding of what the original text says. And yet, as you can see from the discussion above, knowledge of the original -- while wonderfully valuable -- does not solve all or even most problems of translation.
Any translation of Ps 41:1 that limited the reference of "him" to just biological males has missed the point. Anyone -- man, woman, child -- who takes the poor into account will be delivered by the Lord. And an "accurate" translation should use words in such a way as to communicate that.
Hope this helps.