There are basically two scenarios:
If your apps are only doing queries on the database (through views), you could simply update your views to work with "old-style" an "new-style" docs equally. You could then update your documents in the background (eg by following the _changes feed) and eventually remove support for old-style docs again.
If you apps use the structure of the apps, then there will probably be no way around updating the apps as well. Otherwise you'd need to have some proxy in between that translates between old and new style documents, eg
CouchDB with new-style docs <-- proxy application --> apps with old-style docs
You could, of course update your app to handle both old and new-style docs, so that you can transition your documents gradually.
If you have to re-design access to CouchDB, you might consider update handlers to make future changes more transparent.