I assume that any individual who made multiple trips from Spain to the Americas during colonial times apparently had no intention to settle in the Americas permanently, but rather made return trips from Spain just to trade. I some instances, the records also mention explicitly that an individual was a merchant or a captain.
I did a quick search for the name MUZIO and MUZZIO in the archive (http://pares.mcu.es/). There are no records for these names in the Archivo general de Indias unfortunately (there is one record for a MELE MUZIO, Guillerma in another archive).
The name MUZIO / MUZZIO sounds Italian rather than Spanish to me. I know that Italian traders did engage in trade from Spain to the Americas during colonial times. I do not believe, however, that they were exempted from getting a permit to sail to the Americas, but I am not certain. Being exempted might just be the reason why Italian traders do not show up in the Archivo general de Indias.
Have you considered finding a historical maritime association in Cadiz? Maybe they can help you.