The original manuscript is not extant for “the word(s) of Christ”, but the singular its is extant in 𝓞. The printer’s manuscript originally had the singular word as well as the singular its (prior to Joseph Smith’s editing for the 1837 edition). The 1830 typesetter accidentally replaced the singular word with words but left the its (giving the anomalous 1830 reading “the words of Christ / if we follow its course”). In his editing for the 1837 edition, Joseph changed the singular its in 𝓟 to their (but left the singular word unchanged in 𝓟).
The consistent use of the singular (“the word of Christ / if we follow its course”) is the correct reading, especially since in the previous verse we have another reference to “the word of Christ”:
Elsewhere in the text, the plural form (“the words of Christ”) dominates (with at least ten instances), but there are three firm cases of “the word of Christ” (2 Nephi 31:19, 2 Nephi 31:20, and Moroni 7:31). There is also one complicated case in 3 Nephi 29:7, which is discussed there.
Summary: Restore the singular reading in Alma 37:45: “the word of Christ / if we follow its course”); this reading agrees with the singular “the word of Christ”, used earlier in verse 44.