Sounds practical. I’ve done that myself while travelling. Just be sure not to flash it since pickpockets are everywhere in the world, and they’ll be watching.
I’d also bring a few smaller bills ($5,$10, $20’s) for tips and if you just want some 'walking around money without converting a Benjamin.
I suspect (as others here have said) that there will be a place at the departure airport with Argentine pesos available before your flight…Argentina simply doesn’t have the quantity of flights/tourists to make it worth the effort for banks/exchanges to get into the business (IMHO).
Enjoy the trip and the Rugby.