UX is about process and impact, not the artifact.
First, there may be some value in doing a “best practices” evaluation of a website; be sure to document how you went through each step and what you learned from that experience.
On the other hand, just because it’s a self-initiated search doesn’t mean that you don’t have access to users! When you pick a website, it’s entirely possible to do testing. Get friends and family to help you out on the tasks and you’ve got a good small test-base. (Just be sure to structure them well). Additionally, if you’re wanting to do a real test, there are resources out there for recruiting remote testing participants that aren’t that expensive, depending on the size of the task. If you can make it small enough, I’ve had good experience with Mechanical Turk.