It appears that Oliver Cowdery first wrote “the prophets Zenos” in the original manuscript and then did not correct it until months later when he was copying from 𝓞 into 𝓟. The plural s was probably the result of Oliver misinterpreting Joseph Smith’s dictation of “the words of the prophet Zenos”. Oliver was probably expecting “the words of the prophets”, which occurs 14 times in the Book of Mormon. It would have been very difficult to hear the difference between “the prophet Zenos” and “the prophets Zenos”, so it would have been hard to catch this error when Oliver read back the text to Joseph. This kind of s addition sometimes occurs when the following word begins with a sibilant sound (such as /s/, /z/, or /¸s/). Oliver made this same kind of mistake in Alma 41:14 when he took down Joseph’s dictation for “my son see” as “my sons see” (see the discussion under Alma 41:14).
When Oliver Cowdery copied the text for this passage from 𝓞 into 𝓟, he initially wrote “the Prophets Zenos” in the printer’s manuscript. Realizing that the word prophet should be in the singular, he erased the s in the printer’s manuscript, then apparently turned to correct 𝓞 so that it would agree with 𝓟. But for some reason he also crossed out Zenos, as if he were correcting 𝓞 to read “according to the words of the prophets”, a distinct possibility but wrong in this case. Instead of rewriting the name Zenos, Oliver tried to erase the crossout lines, but only at the beginning of the name Zenos. He realized he had correctly copied the name into 𝓟, so it was unnecessary to fully correct 𝓞. In the end, he crossed out the plural s of prophets in 𝓞 with a heavier ink flow. (He probably dipped his pen after having tried to erase the crossing out of Zenos.)
If Oliver Cowdery had crossed out Zenos originally when Joseph Smith was dictating the manuscript, he probably wouldn’t have accidentally written it a second time when producing the printer’s manuscript. It seems very likely that Joseph Smith read off the name Zenos; adding Zenos by accident seems highly unlikely since there is no nearby occurrence of this (or any other) prophet’s name. (The name Zenos last occurred in verse 12, on the previous manuscript page of 𝓞.) Moreover, nowhere else in either manuscript does Oliver Cowdery (or any other scribe) accidentally add a name after writing the word prophet.
Whenever we find the phrase “the words of the prophet” in the text (that is, with the singular prophet), the text does not typically add the name after the word prophet. If the name X occurs, we usually just get “the words of X”, such as “the words of Zenoch”, “the words of Neum”, and “the words of Zenos”, all found earlier in verse 10 of this chapter (and eight other examples elsewhere in the text). Even so, there are a couple of examples where we have “the words of the prophet X”, just as in 1 Nephi 19:16:
Thus all the evidence suggests that the correct reading (“according to the words of the prophet Zenos”) was ultimately transmitted to 𝓟.
Summary: Maintain the current reading in 1 Nephi 19:16, which refers to “the words of the prophet Zenos”; the reading in 𝓞 remains problematic because Zenos appears to be partially crossed out, but was nonetheless transmitted correctly to 𝓟.