Unemployment denial due to quiting?

I currently work for a local small structural pest control company that is making me due agricultural pest control. If caught by city I would have my license taken away. The company has been around for several years so I'm sure they know what they are asking me to do is illegal. They are two different types of pest control and due require different licenses. I don't want to mention this situation to my employer due to fear of retaliation. If i were to quit due to this reason, may I still receive unemployment benefits in California? And if so how would I go about to receive them or what evidence would I need to use in an appeal case.