As a native speaker, I would not consider the use of “one” as a definite pronoun grammatical (except when paired with a previous “one”) - or at least I don’t remember ever having seen it before. “That one” is different but is always used to pick one out of a set of others, unlike in your second example, and in any case using it to refer to a person is very distant.
“They” is much better.
(i’m a fan of Spivak pronouns [original version - e em eir], but i doubt they will ever get even semi-mainstream acceptance)