Legal Question in Business Law in California

How to register a WY LLC is a question for the WY Secretary of State or a WY lawyer. As for your first issue, if you have physical operations in California you will in fact have to register in California. If you form a WY LLC, you will have to register as a foreign LLC doing business in CA, or you can just register as a CA LLC. No state lets you register in one state and then do all your actual business in their state without registering in their state. I'm not sure what kind of "professional" would tell you otherwise.

Many people are under the delusion that a Web-based business formed under the laws of State X and avoid payment of franchise taxes to State Y where the owner/operator lives and works because it is Web-based and therefore lacks any "bricks-and-mortar" presence in Y.

This is a fallacious assumption. A Web-based business is doing business in, and therefore must register and pay franchise taxes to, and and all states where it has significant presence. This would certainly include the state where the owner's hand moves and clicks the mouse.

There is just no way around the plain fact that the franchise tax is charged "for the privilege of doing business in California" and what you'll be doing is exactly that. If you form a WY LLC and run it from a computer in California, you're legally subject to both state's tax and reporting laws, you'll be keeping two sets of books, etc., and it just isn't worth the risk of getting caught.