Neither of those will support Java.
iSwifter, Skyfire, and Puffin are browsers meant to support Flash sites. They are not spectacular, but they will probably work at least to some degree with your site. Opera Mini (free) may also work.
All these browses work at least partially on remote serves, which is how they get around the iPad's lack of support for Flash and Java.
The other choice is to browse using desktop computer through a remote client on the iPad. Splashtop works well and it is cheap. Of course that means you need a dedicated desktop that is always online when you need it, but if you can swing that it's the most versatile solution.