@Rob S Steve is correct; you can use them for dispatches made via Correo Argentino, but NOT via courrier, since people with DNIs (or passports) can use the Puerta a Puerta scheme which these shipments would fall under.
I really don't recommend Correo Argentino given their sticky fingers, and even when they aren't stealing, it takes about 45 days from arrival in the country.
You can get a CDI without residency, but I'm not sure if the procedure is worth the bureaucracy to you.
Screenshot is from Tiendamia
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