The map was from a 1942 LIFE MAGAZINE article, along with these images.
(https://i.imgur.com/NqSA2it.jpeg)
(https://i.imgur.com/My3yZtJ.jpeg)
(https://scontent-lga3-2.xx.fbcdn.net/v/t39.30808-6/454005180_122164650710224076_2570228265827392517_n.jpg?_nc_cat=104&ccb=1-7&_nc_sid=aa7b47&_nc_ohc=K7lL1u9PX3gQ7kNvgEpkgK8&_nc_ht=scontent-lga3-2.xx&oh=00_AYCC8xox7kIW7mkW62_YuorGwSudUlzWs8IQHWlH2hHtkg&oe=66B803D7)
Given the Axis penchant for being driven to seize oil hubs they could not neutralize, I could see a MALTA / LEROS style Fallschirmjaeger operation launched on Aruba as soon as the Axis were established on the South American coast.
Maybe a larger or sustained attack would have been successful. Also would have threatened traffic through the canal or the canal itself.
I suspect the Usual Suspects would have played their part.
(https://i.imgur.com/ZhEYxPb.jpg)