While I would never dare to write applets for the forms you describe, you probably know better. You want an applet, you have it.
Now you want to get rid of the servlet. You can do it, and do away with it for a while. But if you are going to support and evelop the application, it will soon become a nightmare. You will actually have (or be tempted) to develop your own protocol to communicate between your applet and whatever is on the server side.
Then some day someone comes and asks you to add security. Are you going to start using SSL instead of practically transparent HTTPS?
On the other hand, this might be exactly what you want to do to this project, who knows...