10k is legit... get a small traveling money pouch... tie it to your belt and stuff it down you pants. Try to get mostly large bills, maybe a few 50s and 20s. Keep 200 dollars in smaller bills in your pocket, you might need it....
EZE, Terminal A, once you get passed customs keep walking until you are passed final set of doors... take a right... follow the path... there is an official airport taxi on your left hand side. The ride will cost you about 200-240 pesos... nice and safe.
Don't be nervous... It's like any other airport, keep your belongings tight and don't leave anything unattended.
Have a safe trip.