Generally people are not liable for the criminal acts of others. I had a similar thing happen years ago and my company wanted to do the same thing. I told them what you just said bout not wanting my insurance rates to go up, and they agreed to pay the whole thing. Your company's insurance policy likel has a deductible far over the $1,000 price tag, so they will be paying the whole thing out of the bottom line.
The better question of whether you CAN win in small claims court is, do you WANT to win in small claims. For sake of argument, I will assume that you have a $500 deductible. Do you really want to sue your employer over $600? If you do, what is the chance that they find a reason to eliminate you or your job?