Okay, unless I'm completely and utterly misunderstanding how the rules work, you can only wield two weapons if the one in your off-hand has the dual-wielding property. The property is mandatory for your off-hand but completely irrelevent in your main hand.Dual-Wielding just lets you use a bonus action for another attack with that weapon. I can't see anywhere that says you can't use a weapon in your off hand for other purposes, or even for an extra attack if you have one. Just have the scimitar in your main hand, use the short sword for parrying, and your bonus action for something else.
None of the other properties care whether a weapon is primary or secondary, but that one absolutely does. You can have a shortsword in your primary hand and a scimitar in your off-hand--but not the other way around--because only the scimitar has the dual-wielding property. Other than the fact that one method of wielding the weapons is legal and one is illegal, there would be no other difference to doing so, and the remaining properties (which don't care about whether the weapon is primary or secondary) would all function.