TL;DR: disable the Java Plug-in in Safari Preferences Security, and disable the Java plug-in in any other browsers you are using. Done.
Java is installed by default in OS X up through OS X 10.6, and can be optionally installed on 10.7 and 10.8.
Java cannot be removed via any supported means short of a reinstallation, once it is installed.
The Java plug-in is automatically disabled in recent releases (when not used), and the Java plug-in has been additionally and explicitly locked out through Apple's Xprotect update; no recent systems can run Java plug-in right now. (The Java Plug-in is different from Java. Java still works, and has not been disabled.) (The Xprotect mechanism has been part of OS X for a while now, but details from Apple are sparse. Here's a 10.6 Xprotect discussion from Sophos. I don't know the status of Xprotect on 10.6 in conjunction with Java Plug-in; I haven't checked a 10.6 box.)
Apple has provided a similar Xprotect-based mechanism for disabling vulnerable versions of the Adobe Flash Player plug-in, too.
You can easily disable the Java plug-in (which is at the root of the current mess) through the Safari Preferences menu. Safari.app > Safari > Preferences > Security > uncheck "Enable Java". This will avoid the current mess.
Since you're interested in the security of Java, also confirm your Adobe Flash Player is current, or consider removing it. (Unlike Java, the Adobe Flash plug-in can be removed, and there is an uninstaller available form the Adobe web site.)
With newer versions of Safari, you can consider using a Safari extension that blocks the various plug-ins, until you explicitly request loading the window. ClickToPlugin is one.
If your footer is correct, you're running on an old OS X release, which means you don't get various enhancements and updates. Consider an OS X 10.7 upgrade, if your system hardware and software supports it.