Sorry, don't know that one with certainty.
My secondhand-from-reading best guess is - Yes - less damage, but not as much less as you might think. Slash damage is %DPS based. The general consensus in the forums is that special DPS-based damage is only calculated from the right-hand weapon.
So, probably, you would at most lose the unmodified strike value of your left hand weapon, while getting the full Slash damage as calculated off the right-hand weapon.
It is entirely possible, despite the animation, that the left-hand weapon is not conrtibuting anything at all to the damage during a Slash Skill attack. If so, you would not be losing anything.
Since Slash is the Destroyer beginning Skill, why don't you create a couple of new characters and experiment. One with two weapons, one with weapon + shield. Results won't be exact (unless using the editor or console extensively to pre-set the characters), since you have to develop the characters a little to set up the comparison, but it should be enough to get a good working impression of the impact.