No you cannot apply for a working visa at the Airport! The visa at the point of entrée only allows you to enter Cape Verde for a period of time, may be 2weeks or a month!
When you already inside Cape Verde, you can go to the nearest immigration office to extend your visa, or apply for residence permit! You cannot apply for a work permit until you get the job! When you get the job, it's either the company that would apply for you, or then you can go and apply your self, its not difficult like in Europe.
Sorry, some information that I am giving you on here might not be 100% accurate as I no longer live in Cape Verde. I live in Gambia.
But what I am sure is that you do not need a visa to fly to Cape Verde, but at arrival, you will have to pay for the entrée visa. When you settle in, you can extend your visa, or get resident permit! This I know for sure. As for job, I am not sure about it! You can start applying online, but I know for sure that Cape Verde don't have much expatriates jobs. Most are voluntary decisions that might lead to a permanent job.
Lastly, you could first visit, and see how the country is, then you can make up your mind! In Gambia, i am sure you can get a nursing job, because their are so many expatriates vacancies here in their hospitals, i am not aware of Cape Verde anymore.
Thank you and Good luck
