It's all plain text, so just use a normal search-and-replace.
org-mode manages to suppress that somehow, just temporarily change the major mode. e.g. M-x
Actually, assuming you're on Emacs 24.1+,
occur-edit-mode will be a nice way to do that, as you'll see the plain text link syntax in the occur buffer, and only the lines you're interested in.
<regexp> RET (for whatever pattern matches the links you want to edit)
- Switch to the
- e (enter
- Do any editing you need to do. Search and replace, etc. (n.b. You'll need to move point down off the first line of the occur buffer.)
- C-cC-c (confirm the changes and exit
- Return to and save the original buffer.
If you aren't picky about which links you're searching for, you could run a command like this:
(defun my-org-links-occur ()
"Run `occur' for all `org-mode' links in the current buffer."