I would take Extra Arms for 2XP - it's not like the robot literally has 4 arms, but rather the Trait just represents in this case that each of the robot's two arms has the strength of two normal arms.
Of course that is best if you want the robot to also have Ambidexterity in order to dual-wield two 2-handed weapons.
EDIT - Nope, Andrea himself reminded me that Ambidexterity only covers 1-handed weapons!
I think you can just give a robot (or cyborg for that matter) a built-in 2-handed weapon. The only thing is, the Character must keep the other hand free and functional in order to use that built-in weapon.
EDIT - Nope, Cyber Weapon also specifies 1-handed weapons only. So the remaining solution is to take Torso Weapon Mount. Bonus: actually requires no hands!
As to the weapon size issue - I'm not sure you have that quite right: The exception is, a Character can use a 1-handed melee weapon made for someone one size larger than herself using two hands at -1 mod. Otherwise, outsized weapons are of no use. I'm not sure whether "outsized" here also covers undersized but in any case, the relevant exception only covers 1-handed melee weapons.