if you don't want to record the results of a Hot Potatoes quiz, or any other kind of quiz, you could add it to the Moodle course as a "resource", instead of a HotPot activity. Moodle would then treat it as just another webpage and the "results" of the quiz, if there were any, would never leave the student's browser.
I'm afraid I can't suggest any alternatives to Hot Potatoes, because I haven't come across anything which is even half as good. I think it is far and away the best piece of software in its field. I think the same about Moodle too - of course
all the best