Do I lose anything with an empty offhand?

Solution 1:

You should equip a shield in your off hand if you have no comparable weapons.

You get a 15% attack speed boost for equipping two weapons, but you alternate attacks with one, then the other. This means that if the weapons are comparable, you get bonus damage, but if one weapon is significantly better, the time wasted attacking with the lesser weapon will actually decrease your DPS.

If you only have a single weapon equipped, you don't get the attack speed boost, but you do attack with your good weapon every attack. You do not lose any attack speed by equipping a shield, so you might as well find one (no matter how lame it is), because it's better than nothing.