Visual Browser is now available as an Java Applet. This means that you do not have to install it. Visual Browser runs directly in the web browser window.
Self-signed certificates are considered a security risk. You can use my public key and/or you can add http://nlp.fi.muni.cz to the list of exceptions in your Java settings (run "Configure Java", select the Security tab, click on Edit Site List). More information about self-signed certificates can be found at Oracle Documentation.
Java Applets are designed to make users of web browsers feel secure. This means, Java Applets have not all abilities that other applications have. Security restrictions concern access to the filesystem. Since Visual Browser displays data stored in files, it has a digital signature, by accepting it, you can run the application and the application can load files.