Scribe 2’s initial s in the original manuscript looks like an undotted i, so that sword looks like it begins with a four-stroke w (rather than the expected three-stroke w). Yet nearby examples of s-initial words clearly show that we have sword in the original manuscript and not word. (See, for instance, saw and seed on line 38 of page 19 in 𝓞, five lines below sword.) When Oliver Cowdery copied from 𝓞 into 𝓟, he misread the strange looking sw as simply a w, thus leading to the current reading, word.
There are no other examples of “the word of justice” in the Book of Mormon text, but there are seven other examples of “the sword of justice”:
The last example has precisely the same phraseology as the original reading in 1 Nephi 12:18 (“yea even the sword of the justice of the eternal God”).
This parallel from Ether also supports the definite article the before justice. Originally in 𝓞, scribe 2 wrote “the sword of justice”, but then he supralinearly inserted the the. The level of ink flow for the the is somewhat heavier, but it is the same as the ink flow for the following phrase (“of the Eternal God”), which means that scribe 2 dipped his quill after writing the word justice, then inserted the the and continued writing the text.
Summary: Replace word with sword in 1 Nephi 12:18; 𝓞 actually reads this way, and elsewhere the text refers to “the sword of justice”, never to “the word of justice”.