Would i move faster running with like a sword instead of a mace or like glass weapon instead of a material heavier?
Short answer - No. Ony exeption is bow which make you a bit faster.
Your base walking and running speed will be changed if you are in a Werewolf or Vampire Lord form.
Weapon type does not affects your mobility. However if your weapon make you weight over your capacity it might be unable to run.
In ES 5 SKYRIM, the weapon weight does effect your jogging speed, I don’t know about swords vs. axes and maces( I don’t use the last two), but usually the material does.like daedric and Falmer weapons make you jog slower than let’s say a glass or a steel sword. It even says it in one of the loading screens with the dwemer in dwarven armor, sword, and shield.” Carrying heavier weapons or armor will make you move slower.”