There is no hard requirement for the CCSK in order to obtain the CCSP certification.
I am not sure where you may have got this impression. Probably from the fact that practically speaking, the content found in the CCSK is a kind of "subset" of the content found in the CCSP, and both are prepared by/in collaboration with the Cloud Security Alliance.
While it is true that most content can be overlapping (i.e. the CSA Security Guidance, the CSA CCM, etc.), the structure and type of questions you find in the CCSP is really different. From what some people have testified, the biggest help in passing the CCSP has been studying for the CISSP before that - more than studying for the CCSK; this is really because of the way the exam is structured by the (ISC)2, but also because of the content itself.
The CCSP is clearly more complete, but also more expensive. CCSK is a kind of nice badge if you did an earlier version (like v2 or v3) as it testifies that you were an "early adopter". If you go for CCSK v4, it has more updated content which may overlap less with the CCSP as the latter is slower in updates (it won't contain any GDPR for instance). CCSK is definitely cheaper and it less prestigious, as you can obtain it basically by reading a couple of PDF documents and taking the exam from home from your web browser, open book. So, you get the idea of what is worth (I am not suggesting it is worth nothing, but clearly the CCSP is on another level. Of course, you pay for that level).
It is hard to say what is best for you, and you should do your research and decide what is best for your career, based on the information you collect.
I hope it helps.
