I want to export a document that has hyperlinks to files on my computer. Can I export it and keep the hyperlinks to other files?

Changing the document to use relative paths instead of absolute paths to the linked files is only part of the solution.

If the linked PDFs are only on your computer, then anyone trying to use the hyperlinks will have to be able to access your hard drive. That means you must configure file sharing over the company network and give access permission to the other people. The hyperlinks would have to use the UNC (\\server\folder path\file) convention to address the location on your computer. These would be absolute paths. Also note that this would be useless for anyone who isn't connected to your network, for example a laptop user who has left the building, or a subcontractor who doesn't have access rights.

The alternative is to distribute both the document full of hyperlinks and all the PDF files they point to. In that case, the PDFs would be in the same folder as the document (or maybe in a subfolder of that folder), and the hyperlinks would be relative ones pointing to that location.