The original Book of Mormon text frequently used the simple past-tense form of the verb for the past participle. Here in Mosiah 7:13 the earliest text read “I should have wore these bands” rather than the standard “I should have worn these bands”. The standard participial form worn was adopted by the RLDS text in 1874; it first entered the LDS text in the 1906 large-print edition. The verb wear is rather infrequent in the Book of Mormon text, and there are no other examples in the text of either the simple past tense or the past participle for the verb wear. (I exclude from consideration the adjectival use of worn in Alma 20:29: “and their skins were worn exceedingly”.) For a complete discussion of other verbs that originally took the simple past-tense form for the past participle, see past participle in volume 3.
Summary: In accord with the earliest textual sources, accept the use of the simple past-tense form wore as the past participle for wear in Mosiah 7:13; such usage is characteristic of the original Book of Mormon text.