My first thought was pellet gun... lot quieter, and way safer. Solves the woodpecker problem just as well as a .22 without worrying about a projectile carrying 1/2-mile beyond.
We had a similiar problem on a EIFS (Stucco) siding we did for a guy. Woodpeckers put 32 holes all around the house just under the soffit. He's trying to get his insurance to pay for it but doesn't look good. The only siding I haven't seem the peckers (pun intended) get through is steel.
Second time offering this advice on BHC today. If you are going to do something illegal, don't put it on the internet. Brought to you by our friends at useyourhead.org.
It's just a woodpecker. There's like a million of them. And besides, I won't be taken pics of this trophy bird. He must have gotten word anyhow...have seen him since.
If you can get your hands on some creosote apply it lightly with a rag. Otherwise use kerosene in a spray bottle on the fascia. This will deter the wood/carpenter bees and the peckers. We use it on our old barn in the spring early summer to control the bees and birds.