I had contact to a specialist in Andean languages (thanks very much to her!).
She informed me that the Uru (northern part of the Uru-Chipaya people on Lake Titicaca) word for the sling is "kista" or "k'ista".
The inhabitants of the southern villages of the Uru-Chipaya use the Aymara word q'urawa (they have lived in close contact to the Aymara for a long time).
I tried to add this to the "slings in different languages" Wiki section, but it was obviously too difficult for me.
Btw, the Portuguese word is not "arremesso de funda", afaik, but just "funda", as in Latin. If somebody feels qualified to change it...