Yes, you can use any weapon. However, you do have a higher chance of not missing if you have some skill points in the skill for the type of weapon you are using (projectile, NPW..).
If you were aware there is no hindrance, why did you ask if there was a hindrance??
Normally I would direct you to the Suggestions forum, except that combat is still in super-early stages and this is obviously not a concept that has been overlooked, as it was once reflected in the rules pages prior to being intentionally removed.
Lightsabers are an entirely different animal in that a lightsaber combat skill already exists, which non-Force users are unable to train.
The whole "Weapon Skill level" idea was abolished for this system, now your skill denotes how often and how hard you hit instead of your ability to use said weapon. its just assumed that if you have a PW of 1, you can't shoot most guns well.