How do I export a LibreOffice document as a PDF with working, external hyperlinks?

When I choose "Export as PDF" from the File menu I get a window of PDF Options with the "General" tab selected by default. I will assume for the sake of this answer that this is the same for you as well. If you look toward the right-hand end of the tab bar in that PDF Options window (second to last option just to the left of "Security") there should be a tab labeled "Links".

It strikes me that some of these options are likely to be helpful. I found the option which I have selected "Open with PDF reader application" useful for linking to other PDF documents on my filesystem, but I suspect the option which you are wanting is the one just below that "Open with Internet browser". When I test this with my own system (Linux Mint Debian Edition with LibreOffice) it works as expected, opening the clicked link in Firefox (my default web browser).

Also useful to be aware of is that if you have the "Selection" tool selected in the Okular toolbar then links are NOT clickable, as the assumption here appears to be that you are intending to select text for copy/paste operations. To ensure that your links are actively clickable be sure that you are in "Browse" mode (just to the left of the "Zoom" button on a standard Okular default toolbar).

I hope this works for you as described. :)