In this passage Oliver Cowdery initially wrote records in 𝓟, then erased the plural s. Enough of the s remained, however, that the 1830 typesetter read the word as still having its plural s. Thus all printed editions continue to have the plural records. Since Oliver erased the plural s, the change was immediate; the singular record undoubtedly represents the reading of the original manuscript (which is no longer extant here).
The phrase “keep the record(s)” can have two possible interpretations—either as physically taking care of the record(s) or as writing the record(s). In most instances, either interpretation is possible. And of course, the record keeper usually did both tasks. Oftentimes the singular record is used when the writer is referring to the writing of the history of a people. In the case of Omni 1:9, the writer seems to be referring to the small plates of Nephi, a single record that their forefathers (Nephi, Jacob, Enos, Jarom, and Omni) had commanded them to keep.
In the original text, when the text refers to “keeping the record(s)”, there are 13 occurrences of the singular record and 6 of the plural records:
The example in 3 Nephi 1:3 of the singular record reads in the plural in the LDS text, but the earliest textual evidence supports the singular record. For discussion, see under 3 Nephi 1:3.
Summary: Restore in Omni 1:9 the corrected reading in 𝓟, the singular record (“and after this manner we keep the record”).