The Product Key finder is useful if you have a retail install.
If you have factory pre-install, most users who are advanced enough to clean reinstall using a Windows 7 Installation DVD will know to use the Product key on the COA sticker. If they use a key audited from HD it will also work, but typically with a bit more difficulty.
May I ask why you are wanting to change the Product Key? There is no need to reactivate unless you are clean reinstalling or somehow lost your activation. If so, you should have an Activate Now link at Computer>Properties. You really only need to Change Product Key if you are changing the activation to another license.
In that case, type in elevated command Prompt: slmgr -ipk
followed by a space and Product Key. Then activate at Computer>Properties. SLMgr Commands and Options with Windows Vista Product Key Activation » My Digital Life