First off, find out how much your insurance rates will go up by if you make a claim against your policy. More often than others, your rates go up enough that with your deductable, it isn't worth claiming. That's how insurance companies work.
That said, do give it a try and clean it up yourself once you're done with the insurance company. If you're still considering going through insurance, don't try anything too drastic yourself, especially if you're not skilled in it.