If the client has an LMS then configuring the output for SCORM and sending them that ZIP archive to upload to the LMS should work. The LMS is also a web server and it will first unpack the SCORM ZIP so that file relationships work properly. Using an LMS would seem to be your best option.
Another suggestion: IF the client does not want to use their own LMS for this testing, then get a free SCORM Cloud account and upload your SCORM packages there to test. Invite your client's approvers to view the content on SCORM Cloud so that they can see how it should also work on their own LMS.
SharePoint won't work for this. It's designed to work like a File Server, not an HTTP web server.
Additionally, you cannot just send someone a ZIP archive of Captivate content and hope this will work for them. When they dive inside to find the index.html file and try to run that to view everything working, the relationships between files are broken due to the way ZIP files compress things. This results in the content not working for them. Even if they decompress/extract the content first, in many cases it still will not work because certain things in Captivate HTML5 will not work without a web server or LMS.