This article gives an overview on the music in the Spanish Armade from the XVI until today

https://abcblogs.abc.es/espejo-de-navegantes/otros-temas/la-musica-y-la-armada-en-los-siglos-xvi-xvii-y-xviii.html

However it only briefly mentions shanties, they say that the few attested songs are just regular popular songs that can be found in "cancioneros" from that time. Also that it was in many times standard for the spanish armada to have musicians in the crew so it can also be that shanties never truly developed since music was available. But that is just a hypothesis. I will search a historian in spanish naval history, maybe that will help.