If you report it to the insurance company as a collision with an uninsured, there is potential for everything to backfire.
When you signed your insurance contract, you agreed to assist your insurance company with collecting from any guilty party. First off, they will require a police accident report. But more importantly, you made a decision for the insurance company that you didn't have the right to decide for them. The insurance company provided uninsured coverage for you based upon the fact that they will be able to go after the uninsured driver and possibly recover from them. You decided on your own to rob the insurance company of that ability to recover from the driver. This would give the insurance company the right to deny you coverage for intentionally deciding not to get the driver's information.
The worst part is that you will still be rated as having had a collision, and you could potentially see an increase in your insurance rates -- EVEN if they deny you coverage.
While I don't think lying to an insurance company is a good idea (felony insurance fraud), I do think I might have misread your original post. Did you say you LOST the other driver's information after the accident? That you were so shook up after the accident that you must have misplaced the information in your time of stress?
Anyways, as for your question, you can search for used parts from junkyards using this webpage:
http://www.car-part.com/
Junk yards post their parts there, and this is their index. This is actually what a lot of junkyards use themselves to locate parts when you call in. I've gotten plenty of used parts this way. I even got one junkyard to agree to ship for free at the same price as they listed the part for.