Not admin on the family computer (Which I mostly use.)
And my laptop is ubuntu, and desktop edition is windows-only.
Well then, Opera.
Opera is practically a Chrome imitator, but doesn't have any intentions of blocking Java right now... So just use Opera.
It's not technically Java itself - it's all NPAPI plugins except for things like Silverlight, etc. Java doesn't fall under that etc, because Google aren't whitelisting it. Java provides functionality to change files and a lot more than the average Javascript, HTML5 and PHP applications get. AS such, it's dangerous, and Google don't like it.