The most common version of CC is installed and uses the registry.
The PORTABLE version is always my preferred choice for many reasons,
including that it does not make use of the registry.
An application that uses the registry may be doomed to failure when run on a BOOT CD.
It will probably crash in a heap upon being launched - no attempt to do anything.
This is the first reason for Hiren and UBCD not running CCleaner.
I suggest better luck if you use the portable version.
Much of CCleaners actions are based upon where it expects junk files.
It probably needs to use environmental variables like %SystemDrive% and %AppData%
You will need to determine if your chosen Boot CD provides such variables.
A Linux based boot CD will probably not know which drive is C:\
A windows based boot CD may know which drive to call C:\,
but I believe that information is somewhere in the registry.
You have hurdles to jump over.
A POSSIBLE SOLUTION :-
Use the portable version under real old fashioned DOS (e.g. Windows 98 Command.com)
If that works than you have a chance of creating a Flash Drive with a launch *.BAT file.
This BAT can create equivalents to %SystemDrive% and %AppData% etc. etc., using the relevant hard drive designation you set as being drive C:\, and then the BAT can launch CCleaner to use these equivalent variables.
You can test that under Windows 98 Command.com,
and when it looks good you can try launching the BAT from a boot CD
We do however fall down on the lack of registry information.
I believe at least some application temporary files are only zapped if registry settings indicate the application is installed, and it is possible that nothing will get removed other than what you individually specify by Winapp2.ini and Custom / Include.
Alan