The 1874 RLDS edition dropped the adverbial relative pronoun that here in 3 Nephi 4:5, probably accidentally. The 1908 RLDS edition restored the that. Elsewhere in the text, for similar expressions the that is never omitted after no way:
The critical text will maintain the that in all these cases, including here in 3 Nephi 4:5.
Summary: Maintain in 3 Nephi 4:5 and elsewhere in the text the adverbial relative pronoun that whenever it occurs after no way in the earliest text.