Valuation requires comps, but they can include watches in the same general class, adjusting for condition. One doesn't necessarily get valuation by finding exactly the same watch, with the same case and dial. It's a bit more nuanced than that. And in any case, you don't even have the reference of the watch, so how will you know if it's the same watch or not?
It is often fine to insure a watch with a rider on your homeowner's insurance, or you can insure it separately. The cost isn't too different in most cases. Frankly, most of us would not bother to get separate insurance for a watch like this. If it's lost or stolen, the insurance won't replace the sentimental value. But everyone has a different tolerance for risk.
However, if you are serious about insuring it, you should talk to your insurance agent before you spend too much time coming up with a value, since they may require an official appraisal, in which case you would need to hunt down someone whose appraisal they would accept, and then pay for it to be done. And then you'd need to have the value updated every now and then.
There's no harm in saving old parts. Just keep them safe somewhere.