Well, changing the buttons on the left hand side involves actually modifying code in FitNesse. So that is a bit bigger of a deal to do.
However, I can give you a couple of options.
First, you could give everyone a bookmarket that they can use that will run the current page (and set the debug flag). The following does it :
javascript:cur_loc=location.href;location.href=cur_loc + "?test&remote_debug=true";
Second, is that you might be able to add the same thing to the PageHeader or PageFooter page, so that it appears everywhere. But then there will be the issue of the option being there even though you are not on a test page.
!-<a href="?test&remote_debug=true';">Run Page in Debug Mode</a>-!