Hand speed improves through relaxed technique, efficient movement paths, and repeated fast practice rather than through heavy resistance. Shadowboxing with intent, light resistance work, and reaction drills all help. Tension slows hands far more than weakness does.
A tight shoulder and a clenched arm slow the punch before it starts, because opposing muscles are resisting the movement. Fighters are taught to stay loose and tighten only on impact for exactly this reason. Practising relaxed, then adding snap at the end, usually produces a bigger improvement than any strength exercise.
Punches that travel further take longer. Keeping the hands in a consistent guard position, throwing straight rather than looping, and returning along the same line all reduce the distance and the time. Technical coaching here pays more than physical training.
Punching with heavy weights in the hands changes the movement pattern and loads the elbow and shoulder in a way the joint is not designed for. Keep any added resistance light, use it briefly, and always follow it with unloaded fast repetitions.
Speed work belongs early in a session with full recovery. Fast punches thrown while exhausted are not fast, and they train the wrong pattern.
Looking quick in a fight is partly about seeing things earlier. Partner reaction drills and sparring develop that, and no amount of solo speed work replaces them. See The Nervous System and Athletic Performance.