In theory, all that you need to do is detailed in the manual/Wiki.
There are ways to check for any related files that might be left behind by any uninstalled application (perhaps including the registered user information that you mention) but you should not have to worry about that if you just want to install the latest version of KM.
A pleasure. Do get back to us all if you still have problems. I have always found KM to be very well behaved but of course macros can be naughty sometimes!
Something like this happened to me when I opened Keyboard Maestro. It froze and slowed down, so the only way to fix it was to right-click and delete the offending macro. After closing and reopening the app, the problem was solved.