A more significant change in 1 Nephi 19:4 is the replacement of that with what in the 1837 edition. This change was not marked by Joseph Smith in the printer’s manuscript. Since the two words differ from one another by only a single letter, it is probable that what is a simple typo. More importantly, this change makes a difference in the meaning of the sentence. In the original text, Nephi is saying that “this have I … commanded my people that they should do after that I was gone”—namely, keep a record of the people on the other plates. By replacing that with what, the text no longer specifically refers to record keeping, but rather to some general unspecified instructions regarding what the people should do after Nephi has died. In addition, the what now acts as the direct object of the verb command, with the result that the earlier this is the direct object of only the first verb (that is, do). This means that the verb command is now missing its subject. The substitution of what for that thus created a very awkward sentence, plus an unintentional change in the meaning.
Summary: Restore the reading of the original manuscript: “and now this have I done and commanded my people that they should do”; Nephi specifically commanded his people to continue keeping a record of their history.