Which version of Windows are you on? You don't have to uninstall the earlier version of Classic Shell to update to a newer version of Classic Shell. The newer installer replaces your files and keeps your settings.
Instead of shutting down, try restarting Windows (this is because newer Windows releases do a hybrid shutdown). Restarting does a full boot again. Then see if Classic Shell can be updated by downloading the installer of the latest version from
http://classicshell.net/downloads/latest. If not, then try to uninstall (after restarting Windows) from Control Panel -> Programs and Features. If it still gets stuck, follow the steps below:
Start Registry Editor (regedit.exe) and export this Registry key: HKEY_CURRENT_USER\Software\IvoSoft to a REG file. This is to backup your Classic Shell Settings. Then download the Classic Shell Utility from here:
http://www.classicshell.net/downloads/ and remove Classic Shell. After removing it, merge the REG file and download and install the latest version from here:
http://classicshell.net/downloads/latest. Your older Classic Shell settings should be preserved.