Earlier I wrote that turning on NPAPI plugin support to Chrome is a kind of task for "power users". I have found some instructions how to do it and perhaps it is not that bad. If using Java is still critical, you can give your users short and clear instructions. Which ones?
All the user should do is to go to a special page in Chrome settings, click Enable for NPAPI plugins and relaunch the browser.
First, type in chrome://flags/#enable-npapi in Chrome address bar. Note, you should insert this link explicitly, if you add it to <a> element, it won't work.
Then click Enable:
Then relaunch the browser (no worries, all the tabs will be reopened).
The bad news is that this option won't stay long in the Chrome settings. They will completely remove it in 6 months (i.e. September 2015). By that time you should migrate to HTML5 uploader. I believe we will transfer all critical features from Java to HTML5 uploader.
Meanwhile, we are going to release a quick update with the only modification: when Java uploader is loaded on Chrome, it will display a box with instructions how to bring back Java plugin support. As soon as the Java applet is loaded and fully initialized, the instruction box is automatically hidden. We will do it in the nearest time.UPDATE (Apr 24, 2015): The version number 8.5.10 with this feature is already available. Hopefully it will make things simpler for your users.