What are the negative effects of using a weapon type that you don't have a skill in?

There are no longer any negative effects for using a weapon that you are unskilled with, except that you will not get the benefits from your weapon skill. It used to be that you got a debuff from using a weapon without that weapon's skill, similar to the debuff for dual wielding without the proper skill, but that was removed in an earlier update.

I have actually begun not choosing any weapon skill, as it allows me to choose another useful skill, and I find that the bonus of being able to use any weapon without having to worry about losing skills more than outweighs the loss of bonuses from the weapon skill.