ZFT.....
The implied scenario seems to have changed between your first and second post. ...I was assuming you were talking about your own computer, but now more likely concerns about your own 'history' in passing on a multi-use machine owned by someone else. ...In the case of the latter, you are unlikely to have the Administrative permission/ability to put something like CCleaner onto the hard drive.
Further to Richard's previous point, why not get yourself a USB Flash Drive and use
portable applications on it, like Firefox browser, Thunderbird mail client (and portable versions of just about every type of computer program you can think of). All the 'action', happens within the Flash Drive, with nothing left on the PC it's plugged into. This is highlighted as a key feature on the website.
Portable Firefox.
List of other applications
here.