If you get Java update alerts as often as I do it maybe wise to just wait for the next one. I could be wrong, but the Java program seems to fix all the the associated programs if you have not already fiddled with them.
I use "REVO Uninstaller"...Highly recommended. Free, and unbelievably easy to use. After it removes the program, it scans the computer for all the leftover bits-&-pieces and shows you what and where they are. You then check the Bolded items to remove them, and you're done.