Without knowing very much about CCW, this is how I'd expect core.typed to work.
core.typed works best at namespace granularity. When CCW has a namespace open, there should be a button that calls "check-ns" on this namespace.
core.typed throws a clojure.lang.ExceptionInfo, accompanied by errors like:
CCW should present these errors to the user in the typical Eclipse fashion, with visual cues to the actual error source. Usually line and column number is provided.
There might be an option for automatic type checking along with compilation.
This is optional, but provide a REPL with the type checker always on. This would type check forms implicitly.
Hovering over locals could query core.typed for the type at particular positions. This could get complicated.