Joseph Smith Papers indicates Oliver Cowdery may have been the author of the Three Witnesses statement.
History, circa June 1839–circa 1841 [Draft 2], 25 n 77, The Joseph Smith Papers website, accessed December 28, 2022
[77] The earliest copy of the testimony that follows is found in the printer’s manuscript of the Book of Mormon, in the handwriting of Oliver Cowdery. Cowdery likely was the author of the statement, given his writing abilities and similarities between the document and Cowdery’s 1829 correspondence to JS and Hyrum Smith. The copies of the “Testimony of Three Witnesses” and the “Testimony of Eight Witnesses” that follow match the versions in the second edition of the Book of Mormon. (Book of Mormon, Printer’s Manuscript, 463–464, CCLA; “Testimony of Three Witnesses” and “Testimony of Eight Witnesses,” in Book of Mormon, 1837 ed., [620]–[621]; see also JS Letterbook 1, pp. 4–9.)
Book of Mormon, Printer’s Manuscript, 1829–1830. CHL.
The Book of Mormon: an account written by the hand of Mormon, upon plates taken from the plates of Nephi . . . Translated by Joseph Smith, Jr. Kirtland, OH: Printed by O. Cowdery and Co., for P. P. Pratt and J. Goodson, 1837.
JS Letterbook 1 / Smith, Joseph. “Letter Book A,” 1832–1835. Joseph Smith Collection. CHL. MS 155, box 2, fd. 1.