This may sounds like a brute force method, but it's the best way I've come up with. (I discovered this page when I had the same question myself an hour ago... you could spend all day looking, but sometimes it's just easier to do it and be done with it.)
1) Copy and paste just the cells containing the hyperlinks to a new spreadsheet.
2) Export the spreadsheet, click "Change File Type," select "Save As Another File Type" and save it as a web page (aka an HTML file).
3) Open the web page in your browser and view the source.
4) Copy and paste the source into an text editor.
5) Using the Find/Replace function of the text editor, remove the leading and trailing text of each hyperlink. (In other words, replace said text with nothing: "") Note that this text should be identical for each hyperlink.
6) You should now have a text file with nothing but hyperlinks. Copy and paste as needed back into your original spreadsheet or use however/wherever you wish.