Unless you have already designed the application to exclusively use AJAX in one form or another (REST, JSONRPC etc.) then it's pretty much a complete redesign. The reason is simple: "standard" web applications load up one page at a time from the server, with possibly some bits of javascript thrown in. Pyjamas applications are loaded once, as they are pure javascript.
From that point onwards, unless you want another large javascript "hit", the entire application should use AJAX to fetch any data, including HTML. If that sounds like it's a bit different from "normal" web applications, you'd be right. It's more like "Desktop" application development.
So - you can convert the Django (or other web app) one page at a time, to a format which separates out the data from its display. In other words: by the time you're done, there will be no templates left, only JSONRPC services (or other AJAX service / system). If that sounds like a lot of work, then you can temporarily embed the templates on-demand into iframes, either using a pyjamas.ui.HTMLPanel or by using a pyjamas.ui.Frame widget. If you've been told that Frames are a bad idea, you'd be right in the "normal" web development world, but completely wrong in this "Desktop-like" case. Thanks to the Pyjamas API, it's possible to set width and height and to react to Window Resize events, and thus to change the entire layout of the application depending on the user preferences, requirements, browser type and window size (as is done in the Pyjamas Mail example).