Your subscription probably hasn't completely run out yet or the program hasn't phoned home to find out the subscription is expired.
If you want to delete DWCC, go for it. Though, you can have both versions installed at the same time on the same machine, they're separate programs.
Before you delete DWCC, I would suggest going to Site > Manage Sites > Export to export a .ste of any site's you've created with it. That way, when you install DWCS6, you can just import those .ste files and not have to re-enter all of your site settings manually.
