So, here's the update I promised: I went to Latin Express today to make a pick up from Azimo. The whole thing was done in 10 minutes.
There was only one other lady before me and a security guard checking everyone into the place (locked door policy).
I had to fill out a form as it was my first time there, with basic details (name/address/tel number/occupation etc.) about me and the sender (in my case it was the same details, as I sent it to myself). They told me there was a maximum you can collect of 1900 dollars a month. And that was pretty much that.
I went to the central office in Cordoba and 9 de Julio. It's directly on the street (no galeria).
Anyway, the whole experience was a pleasure, so I'd recommend it.