I'm not clear on whether this runs on OS10.6.7

If you're seeing a particular error with the Java update, please post the details and dialog boxes and messages.

If  > Software Update does not offer the Java update, then you either don't need the update, or you're running a version of OS X prior to 10.6. Given you're reportedly on 10.6, the latter does not apply here.

Starting with 10.7, the Java installation is optional. If you don't have Java installed (on 10.7), then you will not be offered the security patch. If you do try to install the Java patch or otherwise poke at Java, then the 10.7 Java installer can be invoked and you can end up with Java installed; something that you're not using. If you poke at this and get the Java download dialog box, select the Not Now option to avoid the install. (Unless you want Java.)

In general, you'll want to sort out those "various reasons", and get your system upgraded to 10.6.8.

And in general, I'd suggest shutting off Java access in Safari and any other web browsers you're using, and ensuring you either have Adobe Flash Player removed, or you have the most recent version of the Flash Player application available from Adobe.

This patch is available for only OS X 10.6.8 and OS X Lion 10.7.3

Time to upgrade, and to shut off Java in the web browsers prior to completing that upgrade.

There are discussions around with command-line-level details including at f-secure for determining if you've been infested by the most recent round of malware.