The first RLDS edition (1874) inserted the definite article the before one hand, thus increasing the parallelism in this coordinated structure (“on the one hand ... on the other”). The original manuscript is extant here, and there is no sign of a the before one hand. Still, one might wonder if early on in the transmission of the text a the was accidentally omitted as Joseph Smith dictated the text to Oliver Cowdery. Elsewhere in the text, we have three instances of “on the one hand … on the other (hand)”, where the definite article the is repeated:
But there is one other conjunctive example where the (first) hand is not preceded by the definite article (as here in the earliest text for Alma 41:4):
This last example of “on one hand” is extant in the original manuscript, so we have two firm cases in 𝓞 where the definite article is lacking before the (first) hand. The example from Alma 52:31 shows no variation in the textual history, which implies that the 1874 RLDS insertion of the intrusive the in Alma 41:4 was unintended.
Summary: Maintain in Alma 41:4 (and Alma 52:31) the occurrence of “on one hand” without any the before hand; either reading, with or without the the, is theoretically possible, so in each case we follow the earliest textual sources.