Yes, the menu may be disabled:
set disablePopupMenu true
set hideNameInPopUp true
hides the file name and contents in the pop-up menu starting with the
NEXT FILE LOADED.
Search for "popup" in http://chemapps.stolaf.edu/jmol/docs/
But bear in mind that once the file is in the applet, it has already
been downloaded and can be retrieved. Also, the page source code will
reveal the direct url.