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.
Best Answer
The Bad Weapon and Hands Full (the debuff for wielding two weapons without the Dual Weilding skill) do not affect any of your statistics, but instead cause a direct percentage loss to your damage output when using melee weapons.
Bad Weapon reduces damage by 28%.
Hands Full reduces damage by 36%.
I'm not sure how these stack (whether it's a straight 64% drop, or compounded ~54% drop).
See the Bad Weapon page on the wiki if you want confirmation.