are you sure that alert is being generated by "java"? one of the lastest bugs/vulnerabilities that was discovered in "java" is that it doesn't validate "certificates", allowing cyber-criminals to use fraudulent certificates, with their malware/exploit kits, to bypass java's security-features (since "signed" java-apps do not cause any alerts to be generated and are allowed to run freely)..
here is an article about java's failure to validate certificates:
i have never heard anyone else say that they have seen an alert like that that was generated by java.. however, maybe your are using some custom-settings that aren't normally used and so that is why you are seeing the alert when no one else has ever seen it..
you say that you need java for some webpages.. well, sometimes, when using a webpage, i will see a prompt to install java, which i ignore.. i still can use the webpage without having java installed, even though it prompts me to install java, i just don't get the java-graphics, which are superficial..
unless you play games at "pogo.com", you probably don't need to have java installed..
my advice is that, in order to have a more secure computer, you uninstall java, even though that means that you will not be able to play games at "pogo.com"..