You can assign hotkeys by pressing a number while having something selected in the favorites. Simply press the hotkey to get it into the main hand and shift+hotkey for off-hand.
I figured out how to set the hotkey numbers (since it's the same as Oblivion), but as for equipping--that's not how it's working for me at all. Shift-hotkey doesn't change the behavior.
Weapons always show up in the mainhand and replace whatever I have there. No combination of shift/alt/ctrl when setting the hotkey number will cause it to show up in my offhand. In order to get a weapon into my offhand I need to open the favorites menu and right-click it.
Spells always show up in the offhand, unless that particular spell is already in my offhand, in which case it'll show up in my mainhand as well. As far as I can tell there's no way to use a hotkey to make a spell replace my mainhand but not my offhand.
Also, weapon switches require sheathing/unsheathing (makes sense, of course). Spells change instantly.
The system was clearly designed with spellcasting in mind, as is also evident by the fact that you can't attack any faster with an offhand than a mainhand (that is, if you have a dagger in your offhand, you can't attack immediately after a mainhand swing--you have to wait until you would've been able to make a mainhand swing anyway). The only thing I can see a reason to dual-wield weapons for is two-weapon power attacks, or possibly having different enchantments/poisons.