Personal favorite in Recoleta: https://maps.app.goo.gl/PgmPZrs6vSLp6jpz9 Azcuenaga 1193 - GIRARG Money Transfer. Like other businesses (Pago Facil etc.) pays sufficiently close to the blue rate that you will probably not want to bother searching out a cueva. The main trick is to find a location close enough to you for convenient transactions. Safe street, safe place.
To put a stamp on the issue of hand-carrying cash out of the USA, here is what USA US Customs and Border Protection has to say. Note it is not sufficient just to "tell" some agent you are over-carrying.
Members of a family residing in one household entering the United States that submit a joint or family declaration must declare if the members are collectively carrying currency or monetary instruments in a combined amount over $10,000 on their Customs Declaration Form (CBP Form 6059B). Members individually carrying over $10,000 are then required to file a Members FinCEN Form 105. Members of a family residing in one household that submit a joint or family declaration are prohibited from causing others in the group to carry currency or monetary instruments in the group on their behalf, so that no member carries more than $10,000. International travelers departing from the United States with currency or monetary instruments in a combined amount over $10,000 are also required to file a FinCEN Form 105 prior to their time of departure. https://help.cbp.gov/s/article/Article-195?language=en_US
Family is pretty much defined (as implied here but search elsewhere) as people who live together (partners, marrieds, adoptees, children, etc.). As others have noted it could be a huge mistake not to declare cash as the law requires.