Improving hand speed means improving Speed strength, you can do that by doing
- punching with bands
- throwing medicine balls or dumbbells
- shot putting
But, you should also pay attention on the execution of your punching technique.
Buy that i mean you should "throw" your hands through the opponent, initiated or catapulted from the legs via the shoulder, and during this motion you should be as relaxed as possible. When you tense up, you are becoming slower.
The only thing that needs to be tight is your fist and upon impact you should
You can use a small exercise and try to punch through a peace of paper that is attached to a rope or something from the ceiling. if you can rip the paper in half that would be a confirmation of a solid punch. In short, the drill is useful. The piece of paper isn't what causes improvements however. It is the fact that you are consciously trying to hit the paper with a snap (ie. as fast as you can). The best way to become fast is by training fast. This simple logic is seen with the drill.