The Book of Mormon text has examples of both mine hand and my hand—and in equal numbers: eight of mine hand (of which five are in Isaiah quotes) and eight of my hand (of which four are in Isaiah quotes). There has been no consistent editing in favor of my hand, the accepted form in current English. The King James Bible also has examples of both variants (note the variation within the Isaiah passages that are quoted in the Book of Mormon). For discussion regarding mine arm versus my arm, see 2 Nephi 28:32. For a general discussion, see possessive pronouns in volume 3.
In this passage, the archaic mine hand was replaced by my hand in the RLDS text beginning with the 1892 edition. This was probably an unintended change since none of the other instances of mine hand have been altered in the RLDS text (including another one here in verse 47: “and I have stretched forth mine hand”).
Summary: Retain the examples of mine hand in the text, including here in Jacob 5:47.