In the Tom Mix version of Destry Rides Again, he does indeed wear his six-guns,a pair of them, and in fact uses them quite frequently. While he also engages in some hard riding and fisticuffs and refrains from shooting to do harm to his enemies, he does use his weapons to hold and intimidate them. At one point he even fires at a hogtied and disarmed villain to persuade him to confess.
I'm not sure how the previous viewer concluded that Mix's Destry wore no guns, something which might fit the James Stewart and Audie Murphy versions more accurately. Even the Mix version bears little resemblance to the original pulp-magazine creation of Harrison (or "Harry") Destry in Max Brand's serial "Twelve Peers." (The title was changed for book publication to the now famous Destry Rides Again -- "again" being somewhat misleading, as there was no prior story about Destry.) As in most of Mix's films, his character was named Tom, with various surnames, and "Tom" was carried over to all the later incarnations of the character. Action sequences were specifically designed to showcase Mix's personality and his skills in riding, shooting, and fighting; in keeping with his public image,in several scenes in Tom is gentle and charming when dealing with young children, as he was in public appearances; some of this is likewise perpetuated in the later film versions. In fact, in the original serial, Harry Destry is a hero in the eyes of at least one impressionable youngster.
(Some prints of this movie bear the title Justice Rides Again, a change made following, and presumably to avoid confusion with, the Stewart-Dietrich version of the book. The musical stage version starred Andy Griffith, and John Gavin starred in the television series.