To load your own solver dynamically you will need to have your solver and the uvr.jar file (from the SDK) available in your computer's classpath. On Windows and Unix computers this usually involves setting your CLASSPATH environment variable. On the MacOS the solver files belong in the Extensions:MRJ Libraries:MRJClasses folder.
With Internet Explorer and Windows, you will need to jar your files for this to work and put the solver's jar file (and uvr.jar) in the CLASSPATH environment variable or mess with the registry, if you're comfortable with it. The HKEY_LOCAL_MACHINE/Software/Microsoft/Java VM folder has a ClassPath key. Add the full pathname to your jar file and uvr.jar to this semicolon-separated list.
If you have trouble getting your browser to acknowledge your classpath, you can download the whole applet and run it locally with your solver files in the same directory as the rest of the applet files.