Krystee, I know how you feel. I was a nervous wreck to get Jackson neutered at just the THOUGHT of losing him. I don't suffer from anxiety problems but my mom has for years and is currently on medication, so I know what it's like to feel that way sort of.
But, it's something that I think is worth it to do it, and it's SUCH a routine surgery. If you take the extra precautionary, you should feel totally confident in your vet.