I'm fine with it. Sal in BL2 was a blast. Needs some balancing though:
Guns
I don't want it to be a trait or perk that you pick up. Instead, I want it to be a core mechanic that improves with perks (because all things improve with perks):
1) While DW, your spread increases by x% and VATS accuracy decreases by x%.
2) Reload times take x% longer.
Perks
8 Legged Freak: While radiated, you grow extra arms that help out while dual wielding guns, steadying your weapons and helping out with reloading. Decreases spread and increases VATS accuracy by x% while dual wielding and reduces load time by x% when you're suffering from radiation sickness.
Bat outta Hell: Increases fire rate and movement speed (optional, just for flavor) by x% while dual wielding guns.
Melee/Unarmed
With melee and unarmed weapons, your accuracy wouldn't take a dive, but your ability to use both hands on one weapon would weaken some things. For example:
1) Parrying/blocking blocks less damage or has a chance to fail. Fine with either option or even both.
2) "Power strikes" (for lack of a better word) deal x% less damage.
Perks
Two for the show (I can imagine a single handed perk named "One for the Money"): Blocking/parrying while dual wielding instead launches a counter strike with the off handed weapon.