Everyone can use any weapon but you must be able to carry it. Also, if you do not have certain skill levels, you will receive accuracy penalties. There is a skill requirement for every weapon. If your character does not meet the requirements for every level he lacks he loses 15% accuracy and takes 1 fire delay longer to reload. Skill Req is to the one for it's class, ie. An NPW's skill req is obviously NPW. The lightsabers are an exception, as the negative accuracy does not apply if the PC has 25% skill in either Lightsaber Attack or Lightsaber Parry Force Skills. ”
So don't need point in those skills, but if you want to shoot well you do need them.
NOTE: combat is not yet introduced into the game so for the moment you cannot shoot anything.