There are plenty of expats on this board who are looking to bring cash INTO Argentina. It would be easier (and safer) for you to give them the cash here and have them wire their funds to your bank account abroad.
Declaring that you are leaving the country with more than $10K in cash is an invitation for trouble. How many people are going to see that form? Would you tell a complete stranger in Argentina that you have that kind of cash on you? Maybe I have been living here for too long, but I just don't trust strangers here with that kind of information.
Plus you have NO IDEA what they are going to do. Maybe they are going to want to see it and count it. Are you then going to pull out all your cash in the middle of the EZE airport while the AFIP employees count it? Are they going to count it privately or in the open in front of everyone. You know the AFIP/Aduanas desk is right in the middle of the check-in lines, in plain view of hundreds of other people.
This just seems like a very risky plan and despite the fact that I don't know you, from one expat to another, let me just try to discourage you from this. People here, especially in positions of authority, are not to be trusted.