When I equip a weapon that I don't have the skill for, I get the Bad Weapon! status effect. While it says, "Your attacks will be less effective until you get rid of it!", most status effects state what they do and what stats they change, but this doesn't have any more information in the tooltip.
When I'm duel wielding, Vampirism and Dwarven Handshake still proc and I don't notice any change in my primary or secondary stats. So what does Bad Weapon! actually do?
A quick look at the wiki (I'm mostly avoiding spoilers) and a search on Google didn't turn up anything promising.