It appears that the function to call to browse a link in an org-mode file is org-open-at-point
which is bound to C-c C-o
.
Edit: Regarding the follow-up question about opening an org-mode link in a secondary browser, using another function seems to work:
(defun org-open-at-point-with-firefox ()
(interactive)
(let ((browse-url-browser-function 'browse-url-firefox))
(org-open-at-point )))