I'm cheap. I'm a 3rd generation German engineer. I never had any decision in the matter. We're all cheap.
When people call me cheap, I just say "you should meet my father".
You're not "cheap" . . . you're "frugal". And if you're anything like my second generation German-American wife you can tell folks that you are "determined" and not "stubborn" and "methodical" rather than "obsessive." . . . It's all in the way you describe things.