Wanting to correct a couple of things.
First, no one is going to laugh you off the skeet field if you are shooting a short barreled HD type shotgun, but they won't take you very seriously either unless you do start shooting perfect scores. Second, a dot type sight on a shotgun that you are using for a game like skeet is a very bad idea if you actually want to get good at the game. The reason for this is that a dot type sight on a shotgun is only useful if you are using the shotgun like a rifle, like when hunting deer or possibly turkey (turkey because of the extremely tight choke typically used). When shooting clay sports of any kind, the whole idea is to NOT look at your sight. You look at the target, not the sight. You can rest assured that if this type of sight was useful for hitting targets flying through the air, that people would be using them. Trust me, they are not.
Another comment made here was in regards to using a pistol grip shotgun on a skeet or trap field. I seriously doubt that there are many places in California that would allow a shooter to do so. I know at my club, USI in Concord, it is strictly forbidden. I think you might be able to use one on the pistol range if you are shooting only slugs, but that is the only place it might even be possible at my range. I'd be careful to check the rules where you intend to shoot before you try it or you risk being kicked out.